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Operator Algebras and Their Modules: An operator space approach

David P. Blecher and Christian Le Merdy

Published in print:
2004
Published Online:
September 2007
ISBN:
9780198526599
eISBN:
9780191712159
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198526599.001.0001
Subject:
Mathematics, Pure Mathematics

This book presents the general theory of algebras of operators on a Hilbert space, and the modules over such algebras. The new theory of operator spaces is presented early on and the text assembles ... More


Basic theory of operator algebras

David P. Blecher and Christian Le Merdy

in Operator Algebras and Their Modules: An operator space approach

Published in print:
2004
Published Online:
September 2007
ISBN:
9780198526599
eISBN:
9780191712159
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198526599.003.0002
Subject:
Mathematics, Pure Mathematics

This chapter begins with a discussion of operator algebras and unitizations. It then covers some basic constructions, the abstract characterization of operator algebras, universal constructions of ... More


Basic theory of operator modules

David P. Blecher and Christian Le Merdy

in Operator Algebras and Their Modules: An operator space approach

Published in print:
2004
Published Online:
September 2007
ISBN:
9780198526599
eISBN:
9780191712159
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198526599.003.0003
Subject:
Mathematics, Pure Mathematics

This chapter discusses the basics of operator modules. Topics covered include Hilbert modules, operator modules over operator algebras, two module tensor products, module maps, module map extension ... More


Completely isomorphic theory of operator algebras

David P. Blecher and Christian Le Merdy

in Operator Algebras and Their Modules: An operator space approach

Published in print:
2004
Published Online:
September 2007
ISBN:
9780198526599
eISBN:
9780191712159
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198526599.003.0005
Subject:
Mathematics, Pure Mathematics

This chapter studies operator algebras ‘up to isomorphism’ or ‘up to complete isomorphism’. Topics covered include homomorphisms of operator algebras, completely bounded characterizations, examples ... More


Tensor products of operator algebras

David P. Blecher and Christian Le Merdy

in Operator Algebras and Their Modules: An operator space approach

Published in print:
2004
Published Online:
September 2007
ISBN:
9780198526599
eISBN:
9780191712159
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198526599.003.0006
Subject:
Mathematics, Pure Mathematics

Tensor products and C*-norms play a prominent role in the theory of C*-algebras, in particular in the study of nuclear C*-algebras and semidiscrete (or injective) von Neumann algebras. This chapter ... More


Selfadjointness criteria

David P. Blecher and Christian Le Merdy

in Operator Algebras and Their Modules: An operator space approach

Published in print:
2004
Published Online:
September 2007
ISBN:
9780198526599
eISBN:
9780191712159
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198526599.003.0007
Subject:
Mathematics, Pure Mathematics

This chapter discusses several interesting criteria which force an operator algebra to be selfadjoint. Such results are in some sense ‘negative’ in nature, showing that certain results or themes ... More


Representation Without Taxation: An Unstrenuous Tour of Algebraic Notions

Laura Ruetsche

in Interpreting Quantum Theories

Published in print:
2011
Published Online:
September 2011
ISBN:
9780199535408
eISBN:
9780191728525
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199535408.003.0004
Subject:
Philosophy, Philosophy of Science

This chapter aspires to be an unpunishing introduction to mathematical notions useful for framing and pursuing foundational questions that arise from the unitary inequivalent representations ... More


Interpreting Quantum Theories

Laura Ruetsche

Published in print:
2011
Published Online:
September 2011
ISBN:
9780199535408
eISBN:
9780191728525
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199535408.001.0001
Subject:
Philosophy, Philosophy of Science

QM∞ includes quantum field theory and the thermodynamic limit of quantum statistical mechanics — theories which, unlike the ‘ordinary’ quantum theories typically discussed by philosophers, concern ... More


Multi-particle Spaces

Daniel Canarutto

in Gauge Field Theory in Natural Geometric Language: A revisitation of mathematical notions of quantum physics

Published in print:
2020
Published Online:
December 2020
ISBN:
9780198861492
eISBN:
9780191894374
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198861492.003.0013
Subject:
Mathematics, Applied Mathematics, Mathematical Physics

The fundamental algebraic notions needed in many-particle physics are exposed. Spaces of free states containing an arbitrary number of particles of many types are introduced. The operator algebra ... More


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