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  • © 2011

Classical Summation in Commutative and Noncommutative Lp-Spaces

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Part of the book series: Lecture Notes in Mathematics (LNM, volume 2021)

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Table of contents (3 chapters)

  1. Front Matter

    Pages i-viii
  2. Introduction

    • Andreas Defant
    Pages 1-13
  3. Commutative Theory

    • Andreas Defant
    Pages 15-78
  4. Noncommutative Theory

    • Andreas Defant
    Pages 79-158
  5. Back Matter

    Pages 159-173

About this book

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).

Keywords

  • 46-XX; 47-XX
  • Menchoff-Rademacher type theorems
  • noncommutative $L_p$-spaces
  • pointwise convergence of orthonormal series
  • summation methods of orthonormal series
  • symmetric spaces of operators

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)

Authors and Affiliations

  • Department of Mathematics, Carl von Ossietzky University Oldenburg, Oldenburg, Germany

    Andreas Defant

Bibliographic Information

Buying options

eBook USD 29.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 37.99
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions