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1.
A vectorx in a Hilbert spaceH iscyclic for a bounded linear operatorTHH if the closed linear span of the orbit {T
n
xn0} ofx underT is all ofH. Operators which have a cyclic vector are said to be cyclic.Jordan operators are the infinite direct sums of Jordan cells acting on finite- dimensional Hilbert spaces. Necessary and sufficient conditions for a Jordan operator to be cyclic are given (see Corollary 6). In this case, a dense set of cyclic vectors is exhibited (see Corollary 4). Sufficient conditions for uncountable collections of cyclic Jordan operators to have a common cyclic vector are given and, in this case, a dense set of common cyclic vectors is exhibited (see Corollary 9).Analogues of these cyclicity results for Jordan operators are obtained for compressions of analytic Toeplitz operatorsT
A
FAF on the Hardy spaceH
2 to subspaces (BH
2) invariant for the backward shiftT
z
* whereB is a Blaschke product by showing that such compressions are quasisimilar to Jordan operators. 相似文献
2.
Donald Sarason 《Integral Equations and Operator Theory》2008,61(2):281-298
This partly expository article develops the basic theory of unbounded Toeplitz operators on the Hardy space H
2, with emphasis on operators whose symbols are not square integrable. Unbounded truncated Toeplitz operators on coinvariant
subspaces of H
2 are also studied.
In memory of Paul R. Halmos 相似文献
3.
In this paper we discuss necessary conditions and sufficient conditions for the compression of an analytic Toeplitz operator onto a shift coinvariant subspace to have nontrivial reducing subspaces. We give necessary and sufficient conditions for the kernel of a Toeplitz operator whose symbol is the quotient of two inner functions to be nontrivial and obtain examples of reducing subspaces from these kernels. Motivated by this result we give necessary conditions and sufficient conditions for the kernel of a Toeplitz operator whose symbol is the quotient of two inner functions to be nontrivial in terms of the supports of the two inner functions. By studying the commutant of a compression, we are able to give a necessary condition for the existence of reducing subspaces on certain shift coinvariant subspaces. 相似文献
4.
5.
Toeplitz operators and Hankel operators 总被引:2,自引:0,他引:2
Dechao Zheng 《Integral Equations and Operator Theory》1989,12(2):280-299
6.
《Indagationes Mathematicae (Proceedings)》1988,91(3):245-248
Let D(T)⊂X→Y be an unbounded linear operator where X and Y are normed spaces. It is shown that if Y is complete then T is strictly singular if and only if T is the sum of a continuous strictly singular operator and an unbounded finite rank operator. A counterexample is constructed for the case in which Y is not complete. 相似文献
7.
In this paper we discuss an unusual phenomenon in the context of Toeplitz operators in the Bergman space on the unit disc:
If two Toeplitz operators commute with a quasihomogeneous Toeplitz operator, then they commute with each other. In the Bourbaki
terminology, this result can be stated as follows: The commutant of a quasihomogeneous Toeplitz operator is equal to its bicommutant.
Received: 11 March 2008 相似文献
8.
9.
Gerard J. Murphy 《Integral Equations and Operator Theory》1997,27(4):439-445
An aspect of the theory of Toeplitz operators on generalised Hardy spaces is considered, namely, a necessary and sufficient condition on the symbols to ensure that the product of two Toeplitz operators is itself a Toeplitz operator. The answer to this question draws on many deep results of the theory of generalised Hardy spaces. 相似文献
10.
Toeplitz operators and algebras 总被引:3,自引:0,他引:3
G. J. Murphy 《Mathematische Zeitschrift》1991,208(1):355-362
11.
Toeplitz operators in n-dimensions 总被引:2,自引:0,他引:2
Victor Guillemin 《Integral Equations and Operator Theory》1984,7(2):145-205
The interplay between the theory of Toeplitz operators on the circle and the theory of pseudodifferential operators on the line (i. e. Wiener-Hopf operators) is by now well-known and well-understood. In this article we show that there is a parallel situation in higher dimensions. To begin with, by using pseudodifferential multipliers, one can simplify the composition rules for Toeplitz operators, (§ 3), and describe precisely how Toeplitz operators of Bergmann type are related to Toeplitz operators of Szegö type (§ 9). Furthermore, it turns out that the ring of pseudodifferential operators on a compact manifold, M, is isomorphic with the ring of Toeplitz operators on an appropriate Grauert tube about M (§ § 4–6), and the ring of Weyl operators on n is isomorphic with the ring of Toeplitz operators on the complex ball in n (§ § 7–10). 相似文献
12.
Sheldon Axler Sun-Yung A. Chang Donald Sarason 《Integral Equations and Operator Theory》1978,1(3):285-309
A sufficient condition is found for the product of two Toeplitz operators to be a compact perturbation of a Toeplitz operator. The condition, which comprehends all previously known sufficient conditions, is shown to be necessary under additional hypotheses. The question whether the condition is necessary in general is left open. 相似文献
13.
We present a unified approach to study properties of Toeplitz localization operators based on the Calderón and Gabor reproducing
formula. We show that these operators with functional symbols on a plane domain may be viewed as certain pseudo-differential
operators (with symbols on a line, or certain compound symbols). 相似文献
14.
In this paper,we construct a function φ in L2(Cn,d Vα) which is unbounded on any neighborhood of each point in Cnsuch that Tφ is a trace class operator on the SegalBargmann space H2(Cn,d Vα).In addition,we also characterize the Schatten p-class Toeplitz operators with positive measure symbols on H2(Cn,d Vα). 相似文献
15.
16.
17.
Kenneth R Davidson 《Journal of Functional Analysis》1977,24(3):291-302
We prove that an operator on H2 of the disc commutes modulo the compacts with all analytic Toeplitz operators if and only if it is a compact perturbation of a Toeplitz operator with symbol in H∞ + C. Consequently, the essential commutant of the whole Toeplitz algebra is the algebra of Toeplitz operators with symbol in QC. The image in the Calkin algebra of the Toeplitz operators with symbol in H∞ + C is a maximal abelian algebra. These results lead to a characterization of automorphisms of the algebra of compact perturbations of the analytic Toeplitz operators. 相似文献
18.
Zhijian Wu Ruhan Zhao Nina Zorboska 《Proceedings of the American Mathematical Society》2006,134(12):3531-3542
We characterize complex measures on the unit disk for which the Toeplitz operator , is bounded or compact on the Bloch type spaces .
19.
Henri-François Gautrin 《Integral Equations and Operator Theory》1988,11(2):173-185
In this paper we study the notion of Toeplitz operators in a Bargmann space; more precisely it is shown that every bounded operator is the uniform limit of Toeplitz operators. We generalize the definition of a Toeplitz operator and show that a large class of operators, which includes the bounded operators, are generalized Toeplitz operators. 相似文献
20.
V. V. Peller 《Journal of Mathematical Sciences》1984,27(1):2533-2539
This paper is devoted to the problem of the existence of invariant subspaces for Toeplitz operators. Let be a Lipschitzian arc in the plane and let f be a non-constant continuous functions on the unit circumference. It is proved that if there exists an open circle such that and if the modulus of continuity f of the function f satisfies the condition then the Toeplitz operator Tf in the Hardy space H2 has a nontrivial hyperinvariant subspace. For the proof of this theorem one makes use of the Lyubich-Matsaev theorem.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 126, pp. 170–179, 1983.I express my deep gratitude to E. M. Dyn'kin for useful discussions. 相似文献