Operator Spaces

The Functional Analysis of Quantum Information Theory - Lecture Notes in Physics ◽

10.1007/978-3-319-16718-3_1 ◽

2015 ◽

pp. 1-37

Author(s):

Ved Prakash Gupta ◽

Prabha Mandayam ◽

V. S. Sunder

Keyword(s):

Operator Spaces

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On some geometric properties of operator spaces

Banach Journal of Mathematical Analysis ◽

10.1215/17358787-2018-0021 ◽

2019 ◽

Vol 13 (1) ◽

pp. 174-191 ◽

Author(s):

Arpita Mal ◽

Debmalya Sain ◽

Kallol Paul

Keyword(s):

Operator Spaces ◽

Geometric Properties

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Globally exact operator spaces

Glasnik Matematicki ◽

10.3336/gm.53.1.12 ◽

2018 ◽

Vol 53 (1) ◽

pp. 179-186

Author(s):

Massoud Amini ◽

◽

Alireza Medghalchi ◽

Hamed Nikpey ◽

◽

...

Keyword(s):

Operator Spaces

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The {OLLP} and $\scr T$-local reflexivity of operator spaces

Illinois Journal of Mathematics ◽

10.1215/ijm/1258138535 ◽

2007 ◽

Vol 51 (4) ◽

pp. 1103-1122 ◽

Author(s):

Z. Dong

Keyword(s):

Operator Spaces ◽

Local Reflexivity

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Parabolic induction, categories of representations and operator spaces

Operator Algebras and Their Applications - Contemporary Mathematics ◽

10.1090/conm/671/13504 ◽

2016 ◽

pp. 85-107 ◽

Author(s):

Tyrone Crisp ◽

Nigel Higson

Keyword(s):

Operator Spaces ◽

Parabolic Induction

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Mapping Spaces and Liftings for Operator Spaces

Proceedings of the London Mathematical Society ◽

10.1112/plms/s3-69.1.171 ◽

1994 ◽

Vol s3-69 (1) ◽

pp. 171-197 ◽

Author(s):

Edward G. Effros ◽

Zhong-Jin Ruan

Keyword(s):

Operator Spaces ◽

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Egoroff’s theorem in measurable operator spaces associated with a Von Neumann algebra

Indian Journal of Pure and Applied Mathematics ◽

10.1007/s13226-018-0283-6 ◽

2018 ◽

Vol 49 (3) ◽

pp. 539-548

Author(s):

Congcong Shen ◽

Lining Jiang

Keyword(s):

Von Neumann Algebra ◽

Operator Spaces ◽

Measurable Operator ◽

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Duality in Operator Spaces

Functional Analysis and Economic Theory ◽

10.1007/978-3-642-72222-6_8 ◽

1998 ◽

pp. 97-100

Author(s):

Victor Lomonosov

Keyword(s):

Operator Spaces

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Operator spaces

Operator Algebras and Their Modules ◽

10.1093/acprof:oso/9780198526599.003.0001 ◽

2004 ◽

pp. 1-48 ◽

Author(s):

David P. Blecher ◽

Christian Le Merdy

Keyword(s):

Operator Spaces

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Distances between Hilbertian operator spaces

Studia Mathematica ◽

10.4064/sm222-1-3 ◽

2014 ◽

Vol 222 (1) ◽

pp. 29-39

Author(s):

Seán Dineen ◽

Cristina Radu

Keyword(s):

Operator Spaces

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On Axiomatizability of Non-Commutative Lp-Spaces

Canadian Mathematical Bulletin ◽

10.4153/cmb-2007-051-7 ◽

2007 ◽

Vol 50 (4) ◽

pp. 519-534

Author(s):

C. Ward Henson ◽

Yves Raynaud ◽

Andrew Rizzo

Keyword(s):

Hilbert Spaces ◽

Normed Space ◽

The Other ◽

Space Structures ◽

Operator Spaces ◽

Infinite Dimensions ◽

Schatten Classes ◽

Lp Spaces ◽

First Order ◽

AbstractIt is shown that Schatten p-classes of operators between Hilbert spaces of different (infinite) dimensions have ultrapowers which are (completely) isometric to non-commutative Lp-spaces. On the other hand, these Schatten classes are not themselves isomorphic to non-commutative Lp spaces. As a consequence, the class of non-commutative Lp-spaces is not axiomatizable in the first-order language developed by Henson and Iovino for normed space structures, neither in the signature of Banach spaces, nor in that of operator spaces. Other examples of the same phenomenon are presented that belong to the class of corners of non-commutative Lp-spaces. For p = 1 this last class, which is the same as the class of preduals of ternary rings of operators, is itself axiomatizable in the signature of operator spaces.

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