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Classical Summation in Commutative and Noncommutative Lp-Spaces

Andreas Defant (Autor)

Buch | Softcover

VIII, 171 Seiten

2011
Springer Berlin (Verlag)
978-3-642-20437-1 (ISBN)

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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).

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
Themenwelt	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