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Operator space tensor norms

Record Type:	Electronic resources : Monograph/item
Title/Author:	Operator space tensor norms by Javier Alejandro Chávez-Domínguez, Verónica Dimant, Daniel Galicer.
Author:	Chávez-Domínguez, Javier Alejandro.
other author:	Dimant, Verónica.
Published:	Cham :Springer Nature Switzerland :2025.
Description:	xv, 189 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Tensor algebra.
Online resource:	https://doi.org/10.1007/978-3-031-96209-7
ISBN:	9783031962097$q(electronic bk.)

Operator space tensor norms
Chávez-Domínguez, Javier Alejandro.

Operator space tensor norms [electronic resource] /by Javier Alejandro Chávez-Domínguez, Verónica Dimant, Daniel Galicer. - Cham :Springer Nature Switzerland :2025. - xv, 189 p. :ill., digital ;24 cm. - Lecture notes in mathematics,v. 23791617-9692 ;. - Lecture notes in mathematics ;2035..

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.

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.

ISBN: 9783031962097$q(electronic bk.)

Standard No.: 10.1007/978-3-031-96209-7doiSubjects--Topical Terms:

348467
Tensor algebra.

LC Class. No.: QA200

Dewey Class. No.: 512.57

Operator space tensor norms
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505 0 $a 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.
520 $a 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.
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