共查询到20条相似文献,搜索用时 11 毫秒
1.
Let F and G be closed subspaces of the complex Hilbert space H, and U and V be closed subspaces of F and G, respectively. In this paper, using the technique of operator block, we present the necessary and sufficient conditions under which (U, V) is a pair of (strictly, non-degenerate) principal invariant subspaces for (F, G). 相似文献
2.
Evgueni Doubtsov 《Proceedings of the American Mathematical Society》2007,135(2):393-395
It is shown that the invariant subspace of the Bergman space of the unit disc, generated by a finite union of Hardy interpolation sequences, is complemented in .
3.
For a backward shift invariant subspace N in H^2(Г^2), the operators Sz and Sw on N are defined by Sz = PNTz|N and Sw, = PNTw|N, where PN is the orthogonal projection from L^2(Г^2) onto N. We give a characterization of N satisfying rank [Sz, Sw^*] = 1. 相似文献
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QIU ZhiJian School of Economic Mathematics Southwestern University of Finance Economics Chengdu China 《中国科学A辑(英文版)》2008,51(1):131-142
Let G be a bounded open subset in the complex plane and let H~2(G) denote the Hardy space on G. We call a bounded simply connected domain W perfectly connected if the boundary value function of the inverse of the Riemann map from W onto the unit disk D is almost 1-1 with respect to the Lebesgue measure on D and if the Riemann map belongs to the weak-star closure of the polynomials in H~∞(W). Our main theorem states: in order that for each M∈Lat (M_z), there exist u∈H~∞(G) such that M=∨{uH~2(G)}, it is necessary and sufficient that the following hold: (1) each component of G is a perfectly connected domain; (2) the harmonic measures of the components of G are mutually singular; (3) the set of polynomials is weak-star dense in H~∞(G). Moreover, if G satisfies these conditions, then every M∈Lat (M_z) is of the form uH~2(G), where u∈H~∞(G) and the restriction of u to each of the components of G is either an inner function or zero. 相似文献
6.
In this paper,we prove the Mohebi-Radjabalipour Conjecture under an ad-ditional condition,and obtain an invariant subspace theorem on subdecomposableoperators. 相似文献
7.
张伦传 《中国科学A辑(英文版)》2002,45(5)
Let A be a separable simple C*-algebra. For each a(≠0) in A, there exists a separable faithful and irreducible * representation (π, Hπ) on A such that π(a) has a non-trivial invariant subspace in Hπ. 相似文献
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Brent J. Carswell 《Proceedings of the American Mathematical Society》2003,131(4):1233-1241
In both the Bergman space and the Hardy space , the problem of determining which bounded univalent mappings of the unit disk have the wandering property is addressed. Generally, a function in has the wandering property in , where denotes either or , provided that every -invariant subspace of is generated by the orthocomplement of within . It is known that essentially every function which has the wandering property in either space is the composition of a univalent mapping with a classical inner function, and that the identity mapping has this property in both spaces. Consequently, weak-star generators of also have the wandering property in both settings. The present paper gives a partial converse to this, and shows that in both settings there is a large class of bounded univalent mappings which fail to have the wandering property.
10.
Alexandru Aleman Stefan Richter Carl Sundberg 《Transactions of the American Mathematical Society》2007,359(7):3369-3407
Let be a Hilbert space of analytic functions on the open unit disc such that the operator of multiplication with the identity function defines a contraction operator. In terms of the reproducing kernel for we will characterize the largest set such that for each , the meromorphic function has nontangential limits a.e. on . We will see that the question of whether or not has linear Lebesgue measure 0 is related to questions concerning the invariant subspace structure of .
We further associate with a second set , which is defined in terms of the norm on . For example, has the property that for all if and only if has linear Lebesgue measure 0.
It turns out that a.e., by which we mean that has linear Lebesgue measure 0. We will study conditions that imply that a.e.. As one corollary to our results we will show that if dim and if there is a such that for all and all we have , then a.e. and the following four conditions are equivalent:
(1) for some ,
(2) for all , ,
(3) has nonzero Lebesgue measure,
(4) every nonzero invariant subspace of has index 1, i.e., satisfies dim .
11.
Let H2(D2) be the Hardy space over the bidisk. For sequences of Blaschke products {φn(z):−∞<n<∞} and {ψn(w):−∞<n<∞} satisfying some additional conditions, we may define a Rudin type invariant subspace M. We shall determine the rank of H2(D2)?M for the pair of operators and . 相似文献
12.
A.F Gualtierotti 《Journal of multivariate analysis》1974,4(3):347-349
We consider the notion of a spherically invariant measure on a real and separable Hilbert space and study some equivalence properties of measures of this type. The latter are of interest in statistical communication theory. 相似文献
13.
In this paper, the backward error of periodic invariant subspaces for regular periodic pairs is defined and its explicit expression is derived. In particular, we also present the expression of the backward error of generalized invariant subspaces for the regular matrix pair. The results are illustrated by two numerical examples. 相似文献
14.
Tavan T. Trent 《Proceedings of the American Mathematical Society》2004,132(8):2429-2432
We find the maximal invariant subspaces for on -valued Bergman-type spaces.
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Invariant subspaces for sequentially subdecomposable operators 总被引:3,自引:0,他引:3
刘明学 《中国科学A辑(英文版)》2003,46(4):433-439
In this paper, using Brown technique, we prove the Mohebi-Radjabalipour Conjecture by strengthening a slight thickness condition of the spectrum, and obtain some invariant subspace theorems. Our result contains an important known invariant subspace theorem as special cases. 相似文献
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Bamdad R. Yahaghi 《Proceedings of the American Mathematical Society》2004,132(4):1059-1066
In this paper we prove the existence of dense-range or one-to-one compact operators on a separable Banach space leaving a given finite chain of subspaces invariant. We use this result to prove that a semigroup of bounded operators is reducible if and only if there exists an appropriate one-to-one compact operator such that the collection of compact operators is reducible.
18.
In this work we consider implementation and testing of an algorithm for continuation of invariant subspaces. Copyright © 2001 John Wiley & Sons, Ltd. 相似文献
19.
Backward shift invariant subspaces with applications to band preserving and phase retrieval problems
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The band preserving and phase retrieval problems have long been interested and studied. In this paper, we, for the first time, give solutions to these problems in terms of backward shift invariant subspaces. The backward shift method among other methods seems to be direct and natural. We show that a function , with , that makes the band of fg to be within that of f if and only if g divided by an inner function related to f, belongs to some backward shift invariant subspace in relation to f. By the construction of backward shift invariant space, the solution g is further explicitly represented through the span of the rational function system whose zeros are those of the Laplace transform of f. As an application, we also use the backward shift method to give a characterization for the solutions of the phase retrieval problem. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
20.
Ming Xue Liu 《数学学报(英文版)》2008,24(9):1471-1474
In this paper, we prove that every operator in a class of contraction operators on a Banach space whose spectrum contains
the unit circle has a nontrivial hyperinvariant subspace.
This research is supported by the Natural Science Foundation of P. R. China (No. 10771039) 相似文献