共查询到10条相似文献,搜索用时 125 毫秒
1.
Brent J. Carswell Christopher Hammond 《Proceedings of the American Mathematical Society》2006,134(9):2599-2605
We prove that any composition operator with maximal norm on one of the weighted Bergman spaces (in particular, on the space ) is induced by a disk automorphism or a map that fixes the origin. This result demonstrates a major difference between the weighted Bergman spaces and the Hardy space , where every inner function induces a composition operator with maximal norm.
2.
Bebe Prunaru 《Proceedings of the American Mathematical Society》1996,124(11):3411-3412
Let be a pure hyponormal operator with compact self-commutator. We show that the unit ball of the commutant of is compact in the strong operator topology.
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This paper concerns the Cesàro operator acting on various spaces of analytic functions on the unit disc. The remarkable fact that this operator is subnormal when acting on the Hardy space H2 has lead to extensive studies of its spectral picture on other spaces of this type. We present some of the methods that have been used to obtain information about the spectrum of the Cesàro operator acting on Hardy and Bergman spaces and give a unified approach to these problems which also yields new results in this direction. In particular, we prove that the Cesàro operator is subdecomposable on H1 and on the standard weighted Bergman spaces , α0. 相似文献
5.
Miroslav Englis Genkai Zhang 《Proceedings of the American Mathematical Society》2006,134(8):2285-2294
Improving upon a recent result of L. Coburn and J. Xia, we show that for any bounded linear operator on the Segal-Bargmann space, the Berezin transform of is a function whose partial derivatives of all orders are bounded. Similarly, if is a bounded operator on any one of the usual weighted Bergman spaces on a bounded symmetric domain, then the appropriately defined ``invariant derivatives' of any order of the Berezin transform of are bounded. Further generalizations are also discussed.
6.
Fernando Leó n-Saavedra Alfonso Montes-Rodrí guez 《Transactions of the American Mathematical Society》2001,353(1):247-267
A vector in a Hilbert space is called hypercyclic for a bounded operator if the orbit is dense in . Our main result states that if satisfies the Hypercyclicity Criterion and the essential spectrum intersects the closed unit disk, then there is an infinite-dimensional closed subspace consisting, except for zero, entirely of hypercyclic vectors for . The converse is true even if is a hypercyclic operator which does not satisfy the Hypercyclicity Criterion. As a consequence, other characterizations are obtained for an operator to have an infinite-dimensional closed subspace of hypercyclic vectors. These results apply to most of the hypercyclic operators that have appeared in the literature. In particular, they apply to bilateral and backward weighted shifts, perturbations of the identity by backward weighted shifts, multiplication operators and composition operators. The main result also applies to the differentiation operator and the translation operator defined on certain Hilbert spaces consisting of entire functions. We also obtain a spectral characterization of the norm-closure of the class of hypercyclic operators which have an infinite-dimensional closed subspace of hypercyclic vectors.
7.
Chunlan Jiang Shunhua Sun Zongyao Wang 《Transactions of the American Mathematical Society》1997,349(1):217-233
It is shown that given an essentially normal operator with connected spectrum, there exists a compact operator such that is strongly irreducible.
8.
Evgueni Doubtsov 《Proceedings of the American Mathematical Society》2001,129(12):3495-3499
We apply Leibenzon's backward shift to show that the composition operator on the unit ball of always maps the weighted Hardy space into the Hardy class .
9.
Stephan Ramon Garcia 《Proceedings of the American Mathematical Society》2005,133(10):3047-3056
We study the backward shift operator on Hilbert spaces (for ) which are norm equivalent to the Dirichlet-type spaces . Although these operators are unitarily equivalent to the adjoints of the forward shift operator on certain weighted Bergman spaces, our approach is direct and completely independent of the standard Cauchy duality. We employ only the classical Hardy space theory and an elementary formula expressing the inner product on in terms of a weighted superposition of backward shifts.
10.
钱忠民 《应用数学学报(英文版)》1994,10(3):252-261
DIFFUSIONPROCESSESONCOMPLETERIEMANNIANMANIFOLDSQIANZHONGMIN(钱忠民)(DepartmentofAppliedMathematics,ShanghaiInstituteofRailwayTec... 相似文献