Classical Summation in Commutative and Noncommutative Lp-Spaces

by Andreas Defant

Overview

The aim of this research is to develop a systematic scheme that makes it possible to transform important parts of the by now classical theory of summation of general orthonormal series into a similar theory for series in noncommutative $L_p$-spaces constructed over a noncommutative measure space (a von Neumann algebra of operators acting on a Hilbert space together with a faithful normal state on this algebra).

Product Details

ISBN-13:	9783642204371
Publisher:	Springer Berlin Heidelberg
Publication date:	07/01/2011
Series:	Lecture Notes in Mathematics , #2021
Edition description:	2011
Pages:	171
Product dimensions:	6.10(w) x 9.25(h) x 0.02(d)

Table of Contents

1 Introduction.- 2 Commutative Theory.- 3 Noncommutative Theory.

Editorial Reviews

From the reviews:

“The book under review is a beautiful and original exposition on the topic of almost everywhere convergent orthonormal series. … The student or researcher who succeeds in reading this book will be rewarded with a deep understanding of the subject, both in the commutative and noncommutative setting. … the book should stand on the shelf of anyone seriously interested in functional analysis and/or probability.” (Stanisław Goldstein, zbMATH, Vol. 1267, 2013)

“This book is well written, with a concise, clear and readable style. It is divided into 3 chapters and includes a preface, a bibliography consisting of 98 items, and symbol, author and subject indexes. … The book is a good source for specialists and graduate students working in functional analysis and operator theory.” (Mohammad Sal Moslehian, Mathematical Reviews, Issue 2012 d)

From the Publisher