Umfang:
1 Online-Ressource (xi, 285 pages)
,
digital, PDF file(s).
ISBN:
9780511862434
Serie:
Cambridge tracts in mathematics 188
Inhalt:
One of the major unsolved problems in operator theory is the fifty-year-old invariant subspace problem, which asks whether every bounded linear operator on a Hilbert space has a nontrivial closed invariant subspace. This book presents some of the major results in the area, including many that were derived within the past few years and cannot be found in other books. Beginning with a preliminary chapter containing the necessary pure mathematical background, the authors present a variety of powerful techniques, including the use of the operator-valued Poisson kernel, various forms of the functional calculus, Hardy spaces, fixed point theorems, minimal vectors, universal operators and moment sequences. The subject is presented at a level accessible to postgraduate students, as well as established researchers. It will be of particular interest to those who study linear operators and also to those who work in other areas of pure mathematics.
Inhalt:
The operator-valued Poisson kernel and its applications -- Properties (An, m) and factorization of integrable functions -- Polynomially bounded operators with rich spectrum -- Beurling algebras -- Applications of a fixed-point theorem -- Minimal vectors -- Universal operators -- Moment sequences and binomial sums -- Positive and strictly-singular operators
Anmerkung:
Title from publisher's bibliographic system (viewed on 05 Oct 2015)
Weitere Ausg.:
ISBN 9781107010512
Weitere Ausg.:
ISBN 9781107010512
Weitere Ausg.:
Erscheint auch als Chalendar, Isabelle, 1970 - Modern approaches to the invariant-subspace problem Cambridge [u.a.] : Cambridge Univ. Press, 2011 ISBN 9781107010512
Weitere Ausg.:
ISBN 1107010519
Weitere Ausg.:
Erscheint auch als Druck-Ausgabe ISBN 9781107010512
Sprache:
Englisch
Schlagwort(e):
Operatortheorie
;
Invarianter Unterraum
DOI:
10.1017/CBO9780511862434
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