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Summing and Nuclear Norms in Banach Space Theory : London Mathematical Society Lecture Notes - G. J. O. Jameson

Summing and Nuclear Norms in Banach Space Theory

London Mathematical Society Lecture Notes

Paperback Published: 28th September 1987
ISBN: 9780521349376
Number Of Pages: 188

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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.

Banach space background
Finite rank operators: trace and 1-nuclear norm
Finite sequences of elements : the quantities µ1, µ2
The summing norms
Other nuclear norms: duality with the summing norms
Pietsch's theorem and its applications
Averaging: type 2 and cotype 2 constants
More averaging: Khinchin's inequality and related results
Integral methods: Gaussian averaging
2-dominated spaces
Grothendieck's inequality
The interpolation method for Grothendieck-type theorems
Results connected with the basis constant
Estimation of summing norms using a restricted number of elements
Pisier's theorem for pi2,1
Tensor products of operators
Trace duality revisited: integral norms
Applications of local reflexivity
Cone-summing norms
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780521349376
ISBN-10: 0521349370
Series: London Mathematical Society Lecture Notes
Audience: Tertiary; University or College
Format: Paperback
Language: English
Number Of Pages: 188
Published: 28th September 1987
Country of Publication: GB
Dimensions (cm): 22.86 x 15.24  x 1.09
Weight (kg): 0.28