Operator space tensor norms / Javier Alejandro Chávez-Domínguez, Verónica Dimant, Daniel Galicer.

Format:

Book

Author/Creator:

Chávez-Domínguez, Javier Alejandro, author.

Dimant, Verónica, author.

Galicer, Daniel, author.

Series:

Lecture notes in mathematics (Springer-Verlag) ; 0075-8434 v. 2379.

Lecture notes in mathematics, 0075-8434 ; volume 2379

Language:

English

Subjects (All):

Operator theory.

Tensor products.

Functional analysis.

Physical Description:

xv, 187 pages : illustrations ; 24 cm.

Place of Publication:

Cham : Springer, [2025]

Summary:

This book provides a comprehensive introduction to the systematic theory of tensor products and tensor norms within the framework of operator spaces. The use of tensor products has significantly advanced functional analysis and other areas of mathematics and physics, and the field of operator spaces is no exception. Building on the theory of tensor products in Banach spaces, this work adapts the definitions and results to the operator space context. This approach goes beyond a mere translation of existing results. It introduces new insights, techniques, and hypotheses to address the many challenges of the non-commutative setting, revealing several notable differences to the classical theory. This text is expected to be a valuable resource for researchers and advanced students in functional analysis, operator theory, and related fields, offering new perspectives for both the mathematics and physics communities. By presenting several open problems, it also serves as a potential source for further research, particularly for those working in operator spaces or operator algebras.

Contents:

Chapter 1. Preliminaries

Chapter 2. Introduction to operator space tensor norms

Chapter 3. Finite and cofinite hulls

Chapter 4. The five basic lemmas

Chapter 5. Dual operator space tensor norms

Chapter 6. The completely bounded approximation property

Chapter 7. Mapping ideals

Chapter 8. Maximal operator space mapping ideals

Chapter 9. Minimal operator space mapping ideals

Chapter 10. Completely projective/injective tensor norms

Chapter 11. Injective/projective hulls and accessibility

Chapter 12. Natural operator space tensor norms

Chapter 13. Conclusions and some open questions.

Notes:

Includes bibliographical references (pages 177-180) and index.

Other Format:

e-book version

ISBN:

9783031962080

3031962087

OCLC:

1545736242

Publisher Number:

9783031962080