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If H is a Hilbert space and T : H ? H is a continous linear operator, a natural question to ask is: What are the closed subspaces M of H for which T M ? M? Of course the famous invariant subspace problem asks whether or not T has any non-trivial invariant subspaces. This monograph is part of a long line of study of the invariant subspaces of the operator T = M (multiplication by the independent variable z, i. e. , M f = zf )on a z z Hilbert space of analytic functions on a bounded domain G in C. The characterization of these M -invariant subspaces is particularly interesting since it entails both the properties z of the functions inside the domain G, their zero sets for example, as well as the behavior of the functions near the boundary of G. The operator M is not only interesting in its z own right but often serves as a model operator for certain classes of linear operators. By this we mean that given an operator T on H with certain properties (certain subnormal operators or two-isometric operators with the right spectral properties, etc. ), there is a Hilbert space of analytic functions on a domain G for which T is unitarity equivalent to M .
| Autorius: | Alexandru Aleman, William T. Ross, Nathan S. Feldman, |
| Serija: | Frontiers in Mathematics |
| Leidėjas: | Birkhäuser Basel |
| Išleidimo metai: | 2009 |
| Knygos puslapių skaičius: | 144 |
| ISBN-10: | 3034600976 |
| ISBN-13: | 9783034600972 |
| Formatas: | 240 x 170 x 9 mm. Knyga minkštu viršeliu |
| Kalba: | Anglų |
Parašykite atsiliepimą apie „The Hardy Space of a Slit Domain“
