Unitary Dilations of Hilbert Space Operators and Related Topics
Author: Béla Szőkefalvi-Nagy
Publisher: American Mathematical Soc.
Published: 1974-01-01
Total Pages: 66
ISBN-13: 9780821888674
DOWNLOAD EBOOK →Author: Béla Szőkefalvi-Nagy
Publisher: American Mathematical Soc.
Published: 1974-01-01
Total Pages: 66
ISBN-13: 9780821888674
DOWNLOAD EBOOK →Author: B. Sz.-Nagy
Publisher:
Published: 1974
Total Pages: 54
ISBN-13: 9781470423797
DOWNLOAD EBOOK →Author: Béla Sz Nagy
Publisher: Springer Science & Business Media
Published: 2010-09-01
Total Pages: 481
ISBN-13: 1441960937
DOWNLOAD EBOOK →The existence of unitary dilations makes it possible to study arbitrary contractions on a Hilbert space using the tools of harmonic analysis. The first edition of this book was an account of the progress done in this direction in 1950-70. Since then, this work has influenced many other areas of mathematics, most notably interpolation theory and control theory. This second edition, in addition to revising and amending the original text, focuses on further developments of the theory, including the study of two operator classes: operators whose powers do not converge strongly to zero, and operators whose functional calculus (as introduced in Chapter III) is not injective. For both of these classes, a wealth of material on structure, classification and invariant subspaces is included in Chapters IX and X. Several chapters conclude with a sketch of other developments related with (and developing) the material of the first edition.
Author: Calvin R. Putnam
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 177
ISBN-13: 3642859380
DOWNLOAD EBOOK →What could be regarded as the beginning of a theory of commutators AB - BA of operators A and B on a Hilbert space, considered as a dis cipline in itself, goes back at least to the two papers of Weyl [3] {1928} and von Neumann [2] {1931} on quantum mechanics and the commuta tion relations occurring there. Here A and B were unbounded self-adjoint operators satisfying the relation AB - BA = iI, in some appropriate sense, and the problem was that of establishing the essential uniqueness of the pair A and B. The study of commutators of bounded operators on a Hilbert space has a more recent origin, which can probably be pinpointed as the paper of Wintner [6] {1947}. An investigation of a few related topics in the subject is the main concern of this brief monograph. The ensuing work considers commuting or "almost" commuting quantities A and B, usually bounded or unbounded operators on a Hilbert space, but occasionally regarded as elements of some normed space. An attempt is made to stress the role of the commutator AB - BA, and to investigate its properties, as well as those of its components A and B when the latter are subject to various restrictions. Some applica tions of the results obtained are made to quantum mechanics, perturba tion theory, Laurent and Toeplitz operators, singular integral trans formations, and Jacobi matrices.
Author: B. La Sz -Nagy
Publisher:
Published: 2011-02-18
Total Pages: 490
ISBN-13: 9781441960955
DOWNLOAD EBOOK →Author: Moshe S. Livsic
Publisher: Springer
Published: 2006-11-15
Total Pages: 116
ISBN-13: 3540478779
DOWNLOAD EBOOK →Classification of commuting non-selfadjoint operators is one of the most challenging problems in operator theory even in the finite-dimensional case. The spectral analysis of dissipative operators has led to a series of deep results in the framework of unitary dilations and characteristic operator functions. It has turned out that the theory has to be based on analytic functions on algebraic manifolds and not on functions of several independent variables as was previously believed. This follows from the generalized Cayley-Hamilton Theorem, due to M.S.Livsic: "Two commuting operators with finite dimensional imaginary parts are connected in the generic case, by a certain algebraic equation whose degree does not exceed the dimension of the sum of the ranges of imaginary parts." Such investigations have been carried out in two directions. One of them, presented by L.L.Waksman, is related to semigroups of projections of multiplication operators on Riemann surfaces. Another direction, which is presented here by M.S.Livsic is based on operator colligations and collective motions of systems. Every given wave equation can be obtained as an external manifestation of collective motions. The algebraic equation mentioned above is the corresponding dispersion law of the input-output waves.
Author: Carl M. Pearcy
Publisher: American Mathematical Soc.
Published: 1974-12-31
Total Pages: 254
ISBN-13: 082181513X
DOWNLOAD EBOOK →Deals with various aspects of the theory of bounded linear operators on Hilbert space. This book offers information on weighted shift operators with scalar weights.