Erling Størmer

• Girard, Mark; Kye, Seung-Hyeok & Størmer, Erling (2021). Convex cones in mapping spaces between matrix algebras. Linear Algebra and its Applications. ISSN 0024-3795. 608, p. 248–269. doi: 10.1016/j.laa.2020.09.008. Full text in Research Archive
• Størmer, Erling (2020). Extension of positive maps. Mathematica Scandinavica. ISSN 0025-5521. 126(2), p. 256–258. doi: 10.7146/math.scand.a-115974. Full text in Research Archive
• Bratteli, Tone; Digernes, Trond; Elliott, George A.; Evans, David E.; Jorgensen, Palle E.T. & Kishimoto, Akitaka [Show all 9 contributors for this article] (2020). Ola Bratteli and His Diagrams. Notices of the American Mathematical Society. ISSN 0002-9920. 67(5), p. 665–675. doi: 10.1090/noti2085. Full text in Research Archive
• Chruscinski, Dariusz; Rivas, Angel & Størmer, Erling (2018). Divisibility and Information Flow Notions of Quantum Markovianity for Noninvertible Dynamical Maps. Physical Review Letters. ISSN 0031-9007. 121(8). doi: 10.1103/PhysRevLett.121.080407. Full text in Research Archive
• Moslehian, Mohammad Sal; Størmer, Erling; Thorbjoernsen, Steen & Winslow, Carl (2018). Uffe Haagerup - his life and mathematics. Advances in Operator Theory. ISSN 2662-2009. 3(1), p. 295–325. doi: 10.22034/aot.1708-1213.
• Størmer, Erling (2017). Mapping cones and separable states. Positivity (Dordrecht). ISSN 1385-1292. p. 1–7. doi: 10.1007/s11117-017-0523-8.
• Størmer, Erling (2017). Positive maps which map the set of rank k projections onto itself. Positivity (Dordrecht). ISSN 1385-1292. 21(1), p. 509–511. doi: 10.1007/s11117-016-0432-2.
• Størmer, Erling (2016). Separable states, maximally entangled states and positive maps. Contemporary Mathematics. ISSN 0271-4132. 671, p. 259–267. doi: 10.1090/conm/671.
• Størmer, Erling (2016). A decomposition theorem for positive maps, and the projection onto a spin factor. Mathematica Scandinavica. ISSN 0025-5521. 118(1), p. 106–118. doi: 10.7146/math.scand.a-23300.
• Buchholz, Detlev & Størmer, Erling (2015). Superposition, Transition Probabilities and Primitive Observables in Infinite Quantum Systems. Communications in Mathematical Physics. ISSN 0010-3616. 339(1), p. 309–325. doi: 10.1007/s00220-015-2405-x.
• Størmer, Erling (2015). The analogue of Choi matrices for a class of linear maps on von Neumann algebras. International Journal of Mathematics. ISSN 0129-167X. 26(2). doi: 10.1142/S0129167X15500184.
• Kawahigashi, Yasuyuki; Ogata, Yoshiko & Størmer, Erling (2014). Normal states of type III factors. Pacific Journal of Mathematics. ISSN 0030-8730. 267(1), p. 131–139. doi: 10.2140/pjm.2014.267.131.
• Størmer, Erling (2013). Separable states and the structural physical approximation of a positive map. Journal of Functional Analysis. ISSN 0022-1236. 264(9), p. 2197–2205. doi: 10.1016/j.jfa.2013.02.015.
• Johnston, Nathaniel; Skowronek, Lukasz & Størmer, Erling (2013). Generation of mapping cones from small sets. Linear Algebra and its Applications. ISSN 0024-3795. 438(7), p. 3062–3075. doi: 10.1016/j.laa.2012.12.007.
• Johnston, Nathaniel & Størmer, Erling (2012). Mapping cones are operator systems. Bulletin of the London Mathematical Society. ISSN 0024-6093. 44, p. 738–748. doi: 10.1112/blms/bds006.
• Skowronek, Lukasz & Størmer, Erling (2012). Choi matrices, norms and entanglement associated with positive maps on matrix algebras. Journal of Functional Analysis. ISSN 0022-1236. 262(2), p. 639–647. doi: 10.1016/j.jfa.2011.09.022.
• Størmer, Erling (2012). Tensor products of positive maps of matrix algebras. Mathematica Scandinavica. ISSN 0025-5521. 111(1), p. 5–11. doi: 10.7146/math.scand.a-15210.
• Størmer, Erling (2011). A completely positive map associated with a positive map. Pacific Journal of Mathematics. ISSN 0030-8730. 252(2), p. 487–492. doi: 10.2140/pjm.2011.252.487.
• Størmer, Erling (2011). MAPPING CONES OF POSITIVE MAPS. Mathematica Scandinavica. ISSN 0025-5521. 108(2), p. 223–232. doi: 10.7146/math.scand.a-15168.
• Størmer, Erling (2010). Entropy in operator algebras. In Blanchard, Etienne; Ellwood, David; Khalkhali, Masoud; Marcolli, Mathilde; Moscovici, Henri & Popa, Sorin (Ed.), Quanta of Maths. AMS and Clay Mathematics Institute. ISSN 978-0-8218-5203-3. p. 601–615.
• Størmer, Erling (2010). Tensor powers of 2-positive maps. Journal of Mathematical Physics. ISSN 0022-2488. 51(10). doi: 10.1063/1.3497628.
• Størmer, Erling (2009). Separable states and positive maps II. Mathematica Scandinavica. ISSN 0025-5521. 105(2), p. 188–198.
• Skowronek, L; Størmer, Erling & Zyczkowski, K (2009). Cones of positive maps and their duality relations. Journal of Mathematical Physics. ISSN 0022-2488. 50(6). doi: 10.1063/1.3155378.
• Størmer, Erling (2009). Duality of cones of positive maps. Münster Journal of Mathematics. ISSN 1867-5778. 2, p. 299–310.
• Størmer, Erling (2008). Separable states and positive maps. Journal of Functional Analysis. ISSN 0022-1236. 254, p. 2303–2312. doi: 10.1016/j.jfa.2007.12.017.
• Størmer, Erling (2007). Multiplicative properties of positive maps. Mathematica Scandinavica. ISSN 0025-5521. 100(1), p. 184–192.
• Størmer, Erling (2007). A reduction theorem for capacity of positive maps. Positivity (Dordrecht). ISSN 1385-1292. 11(1), p. 69–75. doi: 10.1007/s11117-006-2004-3.
• Arveson, William & Størmer, Erling (2007). Asymptotic lifts of positive linear maps. Pacific Journal of Mathematics. ISSN 0030-8730. 233(1).
• Neshveyev, Sergey & Størmer, Erling (2003). Maximal abelian subalgebras of the hyperfinite factor, entropy and ergodic theory. Acta Mathematica Sinica. English series. ISSN 1439-8516. 19(3), p. 599–604.
• Størmer, Erling; Oikhberg, Timur & Rosenthal, Haskell (2003). A predual characterization of semi-finite von Neumann algebras. Contemporary Mathematics. ISSN 0271-4132. 335, p. 243–246.
• Størmer, Erling (2002). Ergodic theory and maximal abelian subalgebras of the hyperfinite factor. Journal of Functional Analysis. ISSN 0022-1236. 195, p. 239–261. Show summary

  Foredraget var om fellesarbeidet med Sergey Neshveyev med samme tittel Dette er fellesarbeidet med Neshveyev, som nå er publisert.

• Neshveyev, Sergey & Størmer, Erling (2002). The McMillan theorem for a class of asymptotically abelian C*-algebras. Ergodic Theory and Dynamical Systems. ISSN 0143-3857. 22(3), p. 889–897.
• Neshveyev, Sergey & Størmer, Erling (2002). Ergodic theory and maximal abelian subalgebras of the hyperfinite factor. Journal of Functional Analysis. ISSN 0022-1236. 195(2), p. 239–261.
• Størmer, Erling (2001). A survey of noncommutative dynamical entropy. In Cuntz, Joachim & Jones, Vaughan (Ed.), Encyclopedia of Mathematical Sciences. Springer. p. 147–198. Show summary

  Artikkelen er en oversikt over teorien fot ikke-kommtativ entropi av automorfier av C*- og von Neumann algebraer fra teoriens begynnelse i 1975 til 2001.

• Neshveyev, Sergey & Størmer, Erling (2001). Entropy of type I algebras. Pacific Journal of Mathematics. ISSN 0030-8730. 201(2), p. 421–428.
• Størmer, Erling (2000). Entropy of endomorphisms and relative entropy in finite von Neumann algebras. Journal of Functional Analysis. ISSN 0022-1236. 170. Show summary

  Vi viser det analoge for entropien til en automorfi av en endelig von Neumann algebra til den klassiske formelen for entropien til en målbevarende transformasjon på et sansynlighetsrom ved relativ entropi.

• Størmer, Erling (2000). Entropy of endomorphisms and relative entropy in finite von Neumann algebras. Journal of Functional Analysis. ISSN 0022-1236. 171, p. 34–52. Show summary

  Vi viser det analoge for entropien til automorfier av endelige von Neumann algebraer til den klassiske formelen, der entropien til en målbevarende transformasjon av et sansynlighetsrom er gitt som relativ entropi.

• Størmer, Erling & Neshveyev, Sergey (2000). The variational principle for a class of asymptotically abelian C*-algebras. Communications in Mathematical Physics. ISSN 0010-3616. 215, p. 177–196. Show summary

  Dette er kopi av prprint med samme tittel. For sammendrag se preprintet.

• Størmer, Erling & Golodets, V. Ya. (1999). Generators and Comparison of Entropies of Automorphisms of finite von Neumann Algebras. Journal of Functional Analysis. ISSN 0022-1236. 164, p. 110–133. Show summary

  We modify slightly Voiculescu´s definition of approximation entropy of automorphisms of finite von Neumann algebras and compare it with the entropy of Connes and Størmer.

• Bratteli, Ola; Kishimoto, Akitaka; Rørdam, Mikael & Størmer, Erling (1993). The crossed product of a UHF algebra by a shift. Ergodic Theory and Dynamical Systems. ISSN 0143-3857. 13, p. 615–626.
• Alfsen, Erik; Shultz, Frederic W & Størmer, Erling (1978). A Gelfand-Neumark Theorem for Jordan Algebras. Advances in Mathematics. ISSN 0001-8708. 28(1), p. 11–56. doi: 10.1016/0001-8708(78)90044-0.

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• Størmer, Erling (2013). Positive Linear Maps of Operator Algebras. Springer Science+Business Media B.V.. ISBN 978-3-642-34369-8. 2013(VII). 134 p.
• Størmer, Erling & Neshveyev, Sergey (2006). Dynamical entropy in operator algebras. Springer. ISBN 3-540-34670-8. 296 p.
• Hanche-Olsen, Harald & Størmer, Erling (1984). Jordan Operator Algebras. Pitman Publishing Limited. ISBN 0-273-08619-7. 191 p.

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• Størmer, Erling (2010). Mapping cones of positive map.
• Størmer, Erling (2010). Positive maps, Choi matrices, and mapping cones.
• Størmer, Erling (2010). Mapping cones of positive maps.
• Størmer, Erling (2010). Mapping cones of positive maps.
• Størmer, Erling (2007). Dynamical entropy in operator algebras. Show summary

  I gave a series of five lectures on noncommutative entropy. Lecture 1: Definitions, Lecture 2, Basic properties, Lecture 3, Crossed products, Lecture 4, The variational principle, Lecture 5, Binary shifts.

• Størmer, Erling (2007). Asymptotisle løftninger og multiplikative egenskaper til positive avbildninger. Show summary

  I outlined work by W. Arveson and myself on positive maps of operator algebras, in pariticular their asymptotic lifts and multiplicative properties.

• Størmer, Erling (2007). Entropy in operator algebras - a survey.
• Størmer, Erling (2006). Multiplicative properties of positive maps. Show summary

  I lectured on multiplicative and asymptotic properties of positive linear maps of operator algebras.

• Størmer, Erling (2006). Multiplicative properties of positive maps of operator algebras.
• Størmer, Erling (2006). Three possible applications of noncommutative entropy. Show summary

  I lectured on possible applications of noncommutative entropy to the following three topics. 1) relative positions of finite dimensional subalgebras in finite von Neumann algebras. 2) entropy characterizations of subsets of the natural numbers via binary shifts, and 3) applications of entropy to indexes of subfactors.

• Størmer, Erling (2005). Capacity of positve maps.
• Størmer, Erling (2004). Positive linear maps and capacity. Show summary

  Foredraget var oversikt over nyere resultater om positive lineæra avbildninger mellom C*-algebraer med anvendelse på begrepet "Capacity" i "quantum computing".

• Størmer, Erling (2004). 1)Entropy in operator algebras 2)Positive linear maps of operator algebras. Show summary

  Jeg holdt to foredrag. Det første var et generelt fordrag for eksperter innen operator algebraer om entropi i operator algebraer. Det andre var om positive lineære avbildninger melom C*-algebraer.

• Størmer, Erling (2004). Positive linear maps of operator algebras. A survey of noncommutatiev entropy.
• Størmer, Erling (2003). Entropy in operator algebras. Show summary

  The lecture was a survey talk for a general mathematical audience on entropy of automorphisms of operator algebras.

• Størmer, Erling (2002). Ergodic theory and maximal abelian subalgebras of the hyperfinite factor. Show summary

  Samme foredrag som jeg holdt ved Abel konferansen i juni 2002

• Størmer, Erling (2002). The variational principle for a class of asymptotically abelia C*-algebras. Show summary

  Fordraget var om fellesarbeid med Sergey Neshveyev med samme tittel

• Størmer, Erling (2002). Ergodic theory and maximal abelian subalgebras of the hyperfinte factor. Show summary

  Foredraget var om fellesarbeid med Sergey Neshveyev med samme tittel.

• Størmer, Erling (2002). Noncommutative entropy and the variational principle. Show summary

  Foredraget var et kollokviumforedrag ved Erlangen Universitet om ikke-kommutativ entropy og den tilhørende teorien for variasjonsprinsippet slik den er utformet av S.Neshveyev og meg selv.

• Størmer, Erling (2001). Maximal abelian subalgebras of the hyperfinite factor, entropy and ergodic theory. Show summary

  Samme som for publikasjonen "Ergodic theory and maximal abelian subalgebras of the hyperfinite factor"

• Størmer, Erling (2001). The McMillan theorem for operator algebraer. Show summary

  Omtrent samme fordrag ved andre anledninger med samme tittel

• Størmer, Erling (2001). Entropy in operator algebras and the McMillan theorem. Show summary

  Samme som for GPOTS konferansen i New Hampshire sist juni

• Størmer, Erling (2001). Noncommutative entropy and the McMillan theorem. Show summary

  F¿rste halvtime av foredraget var en oversikt over teorien for entropien av automorfier av operator algebraer. Den siste halvtimen handlet om fellesarbeidet av Neshveyev og meg selv om McMillan teoremet for en klasse av asymptotisk abelske C*-algebraer.

• Størmer, Erling (2001). The McMillan theorem for a class of asymptotically abelian C*-algebras. Show summary

  Foredraget var om fellesarbeide med Sergey Neshveyev med samme titel

• Størmer, Erling (2001). The McMillan theorem for a class of asymptotically abelian C*-algebras. Show summary

  Forelesningen var om fellesarbeide med Sergey Neshveyev med samme titel

• Størmer, Erling (2000). Tredeling av vinkelen og dobling av kuben, et eksempel på algebrbraisering av geometriske problemer. Show summary

  Jeg viste hvordan problemet med tredeling av vinkelen og dobling av volumet av en kube kan løses ved å se på graden til kropputvidelser av de rasjonale tall oppnådd ved konstruksjon med passer og linjal.

• Størmer, Erling (2000). The variational principle for a class of asymptotically abelian C*-algebras. Show summary

  samme forlesning som gitt ved andre konferanser med samme tittel.

• Størmer, Erling (2000). Entropy in type I algebras. Show summary

  Jeg ga en oversikt over resultater av S.Neshveyev og meg selv om dynamisk entropi i von Neumann algebraer og C*-algebraer av type I

• Størmer, Erling (2000). The variational principle for a class of asymptotically abelian C*-algebras. Show summary

  Foredraget var om fellesarbeid med S.Neshveyev rapportert om tidligere

• Størmer, Erling (2000). The variational principle for a class of asymptotically abelian C*-algebras. Show summary

  Foredraget var over samme emne som ved konferansen i Købehavn i begynelsen av mai.

• Størmer, Erling (1999). A new result on entropy.
• Størmer, Erling (1999). Entropy of endomorphisms and relative entropy in finite von Neumann algebras.
• Størmer, Erling (2007). A reduction theorem for capacity of positive maps. Universitetet i Oslo.
• Størmer, Erling & Arveson, William (2006). Asymptotic lifts of positive linear maps. arXiv:math OA/0611401. Show summary

  We show that the notion of asymptotic lift generalizes naturally to normal positive maps ø: M->M acting on Von Neumann algebras M. We focus on cases in which the domain of the asymptotic lift can be embedded as an operator subsystem of M, and characterize when it is a Jordan subalgebra of M in terms of the asymptotic multiplicative properties of ø.

• Størmer, Erling (2000). A survey of noncommutative entropy. Matematisk Institutt. Show summary

  Artikkelen er en oversiktsartikkel om dynamisk entyropi i operatoralgebraer

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