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).
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." (Stanislaw 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)



Book Information
ISBN 9783642204371
Author Andreas Defant
Format Paperback
Page Count 171
Imprint Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Publisher Springer-Verlag Berlin and Heidelberg GmbH & Co. KG