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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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