Summing and nuclear norms in Banach space theory / G.J.O. Jameson.

Format:

Book

Author/Creator:

Jameson, G. J. O. (Graham James Oscar), author.

Series:

London Mathematical Society student texts ; 8.

London Mathematical Society student texts ; 8

Language:

English

Subjects (All):

Banach spaces.

Banach algebras.

Operator theory.

Physical Description:

1 online resource (xi, 172 pages) : digital, PDF file(s).

Other Title:

Summing & Nuclear Norms in Banach Space Theory

Place of Publication:

Cambridge : Cambridge University Press, 1987.

Language Note:

English

Summary:

This textbook is an introduction to the techniques of summing and nuclear norms. The author's aim is to present a clear and simple account of these ideas and to demonstrate the power of their application to a variety of Banach space questions. The style is expository and the only prerequisite is a beginner's course on Wormed linear spaces and a minimal knowledge of functional analysis. Thus, Dr Jameson is able to concentrate on important, central results and gives concrete and largely non-technical proofs, often supplying alternative proofs which both contribute something to the understanding. Final-year undergraduates and postgraduates in functional analysis will enjoy this introduction to the subject, and there are many examples and exercises throughout the text to help the reader and to demonstrate the range of application these techniques find. A list of references indicates the way for further reading.

Contents:

Operators on finite-dimensional spaces.An application to finite-dimensional spaces; Factorization and extension; The equivalence of v2 and Л2; Further applications; 6. Averaging; type 2 and cotype 2 constants; The basic averaging result and its applications; Vector averaging and a property of hilbert spaces; Type 2 and cotype 2 constants; Averaging operators : a general result on trace duality; 7. More averaging : Khinchin's inequality and related results; Khinchin's inequality; Hubert space version and eolype 2 constant of &x; Applications to 1-summing norms and projection constants

An interpolation theoremSecond proof of grothendieck's inequality; Cotype 2 spaces are 2-dominated; 12. Results connected with the basis constant; The basis constant; Connections with Л1 and the Gordon-Lewis constant; The 2-dominated property and cotype 2; Connections with grothendieck's inequality; Spaces with large basis constants; 13. Estimation of summing norms using a restricted number of elements.; Elementary facts; Estimation of n2 using n elements; The number of elements required for exact determination of Л2; Estimation of Лp for other p.; 14. Pisier's theorem for Л21

15. Tensor products of operators

Notes:

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Includes bibliographical references (p. [170]-172) and index.

ISBN:

1-316-08685-2

0-511-56916-5

1-107-36633-X

1-107-37105-8

1-107-36142-7

1-107-36835-9

1-299-40412-X

1-107-36387-X

OCLC:

668201605