Introduction to Tensor Products of Banach ...

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Sprache: Englisch

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Beschreibung

This book is intended as an introduction to the theory of tensor products of Banach spaces. The prerequisites for reading the book are a first course in Functional Analysis and in Measure Theory, as far as the Radon-Nikodym theorem. The book is entirely self-contained and two appendices give addi tional material on Banach Spaces and Measure Theory that may be unfamil iar to the beginner. No knowledge of tensor products is assumed. Our viewpoint is that tensor products are a natural and productive way to understand many of the themes of modern Banach space theory and that "tensorial thinking" yields insights into many otherwise mysterious phenom ena. We hope to convince the reader of the validity of this belief. We begin in Chapter 1 with a treatment of the purely algebraic theory of tensor products of vector spaces. We emphasize the use of the tensor product as a linearizing tool and we explain the use of tensor products in the duality theory of spaces of operators in finite dimensions. The ideas developed here, though simple, are fundamental for the rest of the book.

Zusammenfassung

This book will be used in graduate courses for those who have studied functional analysis and are moving on to study tensor methods and Banach spaces. Also useful for those studying advanced functional analysis.

Inhaltsverzeichnis

1 Tensor Products.- 2 The Projective Tensor Product.- 3 The Injective Tensor Product.- 4 The Approximation Property.- 5 The Radon-Nikodÿm Property.- 6 The Chevet-Saphar Tensor Products.- 7 Tensor Norms.- 8 Operator Ideals.- A Suggestions for Further Reading.- B Summability in Banach Spaces.- C Spaces of Measures.- References.

Details

Erscheinungsjahr:	2002
Fachbereich:	Analysis
Genre:	Importe , Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Buch
Inhalt:	xiv 226 S. 31 s/w Illustr.
ISBN-13:	9781852334376
ISBN-10:	1852334371
Sprache:	Englisch
Einband:	Gebunden
Autor:	Ryan, Raymond A.
Hersteller:	Springer London Springer-Verlag London Ltd.
Verantwortliche Person für die EU:	Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße:	241 x 160 x 19 mm
Von/Mit:	Raymond A. Ryan
Erscheinungsdatum:	15.01.2002
Gewicht:	0,535 kg