Strong Limit Theorems in Noncommutative L2-Spaces
Strong Limit Theorems in Noncommutative L2-Spaces

Author: Ryszard Jajte

Publisher: Springer

Published: 2006-12-08

Total Pages: 122

ISBN-13: 3540475125

DOWNLOAD EBOOK

The noncommutative versions of fundamental classical results on the almost sure convergence in L2-spaces are discussed: individual ergodic theorems, strong laws of large numbers, theorems on convergence of orthogonal series, of martingales of powers of contractions etc. The proofs introduce new techniques in von Neumann algebras. The reader is assumed to master the fundamentals of functional analysis and probability. The book is written mainly for mathematicians and physicists familiar with probability theory and interested in applications of operator algebras to quantum statistical mechanics.

Classical Summation in Commutative and Noncommutative Lp-Spaces
Classical Summation in Commutative and Noncommutative Lp-Spaces

Author: Andreas Defant

Publisher: Springer Science & Business Media

Published: 2011-06-22

Total Pages: 178

ISBN-13: 3642204376

DOWNLOAD EBOOK

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).

Quantum Probability And Related Topics: Qp-pq (Volume Ix)
Quantum Probability And Related Topics: Qp-pq (Volume Ix)

Author: Luigi Accardi

Publisher: World Scientific

Published: 1994-12-16

Total Pages: 427

ISBN-13: 9814501301

DOWNLOAD EBOOK

Quantum Probability and Related Topics is a series of volumes whose goal is to provide a picture of the state of the art in this rapidly growing field where classical probability, quantum physics and functional analysis merge together in an original synthesis which, for 20 years, has been enriching these three areas with new ideas, techniques and results.

Noncommutative Probability
Noncommutative Probability

Author: I. Cuculescu

Publisher: Springer Science & Business Media

Published: 2013-06-29

Total Pages: 367

ISBN-13: 9401583749

DOWNLOAD EBOOK

The intention of this book is to explain to a mathematician having no previous knowledge in this domain, what "noncommutative probability" is. So the first decision was not to concentrate on a special topic. For different people, the starting points of such a domain may be different. In what concerns this question, different variants are not discussed. One such variant comes from Quantum Physics. The motivations in this book are mainly mathematical; more precisely, they correspond to the desire of developing a probability theory in a new set-up and obtaining results analogous to the classical ones for the newly defined mathematical objects. Also different mathematical foundations of this domain were proposed. This book concentrates on one variant, which may be described as "von Neumann algebras". This is true also for the last chapter, if one looks at its ultimate aim. In the references there are some papers corresponding to other variants; we mention Gudder, S.P. &al (1978). Segal, I.E. (1965) also discusses "basic ideas".

Operator Valued Hardy Spaces
Operator Valued Hardy Spaces

Author: Tao Mei

Publisher: American Mathematical Soc.

Published: 2007

Total Pages: 78

ISBN-13: 0821839802

DOWNLOAD EBOOK

The author gives a systematic study of the Hardy spaces of functions with values in the noncommutative $Lp$-spaces associated with a semifinite von Neumann algebra $\mathcal{M .$ This is motivated by matrix valued Harmonic Analysis (operator weighted norm inequalities, operator Hilbert transform), as well as by the recent development of noncommutative martingale inequalities. in this paper noncommutative Hardy spaces are defined by noncommutative Lusin integral function, and it isproved that they are equivalent to those defined by noncommutative Littlewood-Paley G-functions. The main results of this paper include: (i) The analogue in the author's setting of the classical Fefferman duality theorem between $\mathcal{H 1$ and $\mathrm{BMO $. (ii) The atomic decomposition of theauthor's noncommutative $\mathcal{H 1.$ (iii) The equivalence between the norms of the noncommutative Hardy spaces and of the noncommutative $Lp$-spaces $(1

Recent Advances in Operator Theory and Related Topics
Recent Advances in Operator Theory and Related Topics

Author: Laszlo Kerchy

Publisher: Springer Science & Business Media

Published: 2001-10-01

Total Pages: 726

ISBN-13: 9783764366070

DOWNLOAD EBOOK

These 35 refereed articles report on recent and original results in various areas of operator theory and connected fields, many of them strongly related to contributions of Sz.-Nagy. The scientific part of the book is preceeded by fifty pages of biographical material, including several photos.

Real Functions - Current Topics
Real Functions - Current Topics

Author: Vasile Ene

Publisher: Springer

Published: 2006-11-14

Total Pages: 321

ISBN-13: 3540494006

DOWNLOAD EBOOK

Most books devoted to the theory of the integral have ignored the nonabsolute integrals, despite the fact that the journal literature relating to these has become richer and richer. The aim of this monograph is to fill this gap, to perform a study on the large number of classes of real functions which have been introduced in this context, and to illustrate them with many examples. This book reports on some recent advances in the theory of real functions and can serve as a textbook for a course in the subject, and to stimulate further research in this exciting field.

Seminaire de Probabilites XXIX
Seminaire de Probabilites XXIX

Author: Jacques Azema

Publisher: Springer

Published: 2006-11-14

Total Pages: 337

ISBN-13: 354044744X

DOWNLOAD EBOOK

All the papers included in this volume are original research papers. They represent an important part of the work of French probabilists and colleagues with whom they are in close contact throughout the world. The main topics of the papers are martingale and Markov processes studies.