Classical Summation in Commutative and Noncommutative L<sub>p</sub>-Spaces

  • Andreas┬áDefant

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

Table of contents

  1. Front Matter
    Pages i-viii
  2. Andreas Defant
    Pages 1-13
  3. Andreas Defant
    Pages 15-78
  4. Andreas Defant
    Pages 79-158
  5. Back Matter
    Pages 159-173

About this book

Introduction

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

Authors and affiliations

  • Andreas┬áDefant
    • 1
  1. 1.Department of MathematicsCarl von Ossietzky University OldenburgOldenburgGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-20438-8
  • Copyright Information Springer-Verlag Berlin Heidelberg 2011
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-642-20437-1
  • Online ISBN 978-3-642-20438-8
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • About this book