Kategoria BISAC: Mathematics >> Functional Analysis

Quantum probability and the theory of operator algebras are both concerned with the study of noncommutative dynamics. Focusing on stationary processes with discrete-time parameter, this book presents (without many prerequisites) some basic problems of interest to both fields, on topics including extensions and dilations of completely positive maps, Markov property and adaptedness, endomorphisms of operator algebras and the applications arising from the interplay of these themes. Much of the material is new, but many interesting questions are accessible even to the reader equipped only with...

This volume considers various applications of equimeasurable function rearrangements to the "best constant"-type problems. It presents several classical theorems along with some very recent results. Coverage includes a product-space extension of the Rising Sun lemma, a product-space version of the John-Nirenberg inequality for bounded mean oscillation functions with sharp exponent, and sharp embedding theorems for Muckenhoupt, Gurov-Reshetnyak, and Gehring classes.

In the last decade, convolution operators of matrix functions have received unusual attention due to their diverse applications. This monograph presents some new developments in the spectral theory of these operators. The setting is the L^p spaces of matrix-valued functions on locally compact groups. The focus is on the spectra and eigenspaces of convolution operators on these spaces, defined by matrix-valued measures. Among various spectral results, the L²-spectrum of such an operator is completely determined and as an application, the spectrum of a discrete Laplacian...

Abstract topological tools from generalized metric spaces are applied in this volume to the construction of locally uniformly rotund norms on Banach spaces. The book offers new techniques for renorming problems, all of them based on a network analysis for the topologies involved inside the problem.

Maps from a normed space X to a metric space Y, which provide locally uniformly rotund renormings on X, are studied and a new frame for the theory is obtained, with interplay between functional analysis, optimization and topology using subdifferentials of Lipschitz functions and covering...

This book teams up the spectral theory of bounded linear operators with von Neumann's theory of unbounded operators to provide a framework for the study of stable methods for the evaluation of unbounded operators. The text presents numerous illustrations of unbounded linear operators that arise in various inverse problems of mathematical physics. It also offers an extensive exposition of background material from the theory of operators on Hilbert space.