Classical Summation in Commutative and Noncommutative Lp-Spaces

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).

Includes supplementary material: sn.pub/extras

Inhalt
1 Introduction.- 2 Commutative Theory.- 3 Noncommutative Theory.