Classical Summation in Commutative and Noncommutative Lp-Spaces
Seiten
2011
|
2011
Springer Berlin (Verlag)
978-3-642-20437-1 (ISBN)
Springer Berlin (Verlag)
978-3-642-20437-1 (ISBN)
This book develops a systematic scheme that makes it possible to transfer important parts of the theory of summation of general orthonormal series into a similar theory for series in noncommutative Lp-spaces built over a noncommutative measure space.
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).
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).
1 Introduction.- 2 Commutative Theory.- 3 Noncommutative Theory.
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)| Erscheint lt. Verlag | 22.6.2011 |
|---|---|
| Reihe/Serie | Lecture Notes in Mathematics |
| Zusatzinfo | VIII, 171 p. 17 illus. |
| Verlagsort | Berlin |
| Sprache | englisch |
| Maße | 155 x 235 mm |
| Gewicht | 285 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
| Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik | |
| Schlagworte | 46-XX • 46-XX; 47-XX • 47-XX • Analysis • Menchoff-Rademacher type theorems • noncommutative $L_p$-spaces • pointwise convergence of orthonormal series • summation methods of orthonormal series • symmetric spaces of operators |
| ISBN-10 | 3-642-20437-6 / 3642204376 |
| ISBN-13 | 978-3-642-20437-1 / 9783642204371 |
| Zustand | Neuware |
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