共查询到20条相似文献,搜索用时 78 毫秒
1.
Joel H. Shapiro 《Journal of Mathematical Analysis and Applications》2007,333(1):523-529
Nazarov and Shapiro recently showed that, while composition operators on the Hardy space H2 can only trivially be Toeplitz, or even “Toeplitz plus compact,” it is an interesting problem to determine which of them can be “asymptotically Toeplitz.” I show here that if “asymptotically” is interpreted in, for example, the Cesàro (C,α) sense (α>0), then every composition operator on H2 becomes asymptotically Toeplitz. 相似文献
2.
The composition operators with closed rangc on H2(B
n) are characterized, and the Fredholmness of products of Toeplitz and composition operators discussed. Moreover, using composition
operators, the spectra of Toeplitz operators are studied.
Project supported by the National Natural Sciencc Foundation of China and the Postdoctoral Science Foundation of China. 相似文献
3.
Denote by Ω the Siegel domain in Cn, n 〉 1. In this paper, we study the essential spectra of Toeplitz operators defined on the Hardy space H2(а↓Ω). In addition, the characteristic equation of analytic Toeplitz operators iааs obtained. 相似文献
4.
In this paper, we prove that a composition operator onH
p
(B) is Fredholm if and only if it is invertible if and only if its symbol is an automorphism onB, and give the representation of the spectra of a class of composition operators. In addition, using composition operator,
we discuss intertwining Toeplitz operators.
Supported by NNSF and PDSF 相似文献
5.
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
6.
U?ur Gül 《Journal of Mathematical Analysis and Applications》2011,377(2):771-791
In this work we study the essential spectra of composition operators on Hardy spaces of analytic functions which might be termed as “quasi-parabolic.” This is the class of composition operators on H2 with symbols whose conjugate with the Cayley transform on the upper half-plane are of the form φ(z)=z+ψ(z), where ψ∈H∞(H) and ℑ(ψ(z))>?>0. We especially examine the case where ψ is discontinuous at infinity. A new method is devised to show that this type of composition operator fall in a C*-algebra of Toeplitz operators and Fourier multipliers. This method enables us to provide new examples of essentially normal composition operators and to calculate their essential spectra. 相似文献
7.
We characterize the p-approximation property (p-AP) introduced by Sinha and Karn [D.P. Sinha, A.K. Karn, Compact operators whose adjoints factor through subspaces of ?p, Studia Math. 150 (2002) 17-33] in terms of density of finite rank operators in the spaces of p-compact and of adjoints of p-summable operators. As application, the p-AP of dual Banach spaces is characterized via density of finite rank operators in the space of quasi-p-nuclear operators. This relates the p-AP to Saphar's approximation property APp′. As another application, the p-AP is characterized via a trace condition, allowing to define the trace functional on certain subspaces of the space of nuclear operators. 相似文献
8.
Thomas L. Kriete Barbara D. MacCluer Jennifer L. Moorhouse 《Journal of Functional Analysis》2009,257(8):2378-2409
We determine the essential spectra of algebraic combinations of Toeplitz operators with continuous symbol and composition operators induced by a class of linear-fractional non-automorphisms of the unit disk. The operators in question act on the Hardy space H2 on the unit disk. Our method is to realize the C*-algebra that they generate as an extension of the compact operators by a concrete C*-algebra whose invertible elements are easily characterized. 相似文献
9.
We study some generalized Toeplitz operators associated to operators T on a Hilbert space H, for which there exists the limit of {‖Tnh‖} for every h∈H. We refer to the asymptotic limit ST of such a T, in the sense of [L. Kerchy, Operators with regular norm-sequences, Acta Sci. Math. (Szeged) 63 (1997) 571-605; L. Kerchy, Generalized Toeplitz operators, Acta Sci. Math. (Szeged) 68 (2002) 373-400; G. Cassier, Generalized Toeplitz operators, restrictions to invariant subspaces and similarity problems, J. Operator Theory 53 (1) (2005) 101-140; C.S. Kubrusly, An Introduction to Models and Decompositions in Operator Theory, Birkhäuser, Boston, 1997], and we give some conditions of ergodicity for T. Also, certain results of Douglas [R.G. Douglas, On the operator equation S∗XT=X and related topics, Acta Sci. Math. (Szeged) 30 (1969) 19-32] involving generalized Toeplitz operators are extended in our more general setting, and we apply these results to ρ-contractions. 相似文献
10.
We investigate some problems for truncated Toeplitz operators. Namely, the solvability of the Riccati operator equation on the set of all truncated Toeplitz operators on the model space K θ = H2ΘθH2 is studied. We study in terms of Berezin symbols invertibility of model operators. We also prove some results for the Berezin number of the truncated Toeplitz operators. Moreover, we study some property for H2-functions in terms of noncyclicity of co-analytic Toeplitz operators and hypercyclicity of model operators. 相似文献
11.
Nazih S. Faour 《Rendiconti del Circolo Matematico di Palermo》1986,35(2):221-232
Let ? be an element in \(H^\infty (D) + C(\overline D )\) such that ?* is locally sectorial. In this paper it is shown that the Toeplitz operator defined on the Bergman spaceA 2 (D) is Fredholm. Also, it is proved that ifS is an operator onA 2(D) which commutes with the Toeplitz operatorT ? whose symbol ? is a finite Blaschke product, thenS H ∞ (D) is contained inH ∞ (D). Moreover, some spectral properties of Toeplitz operators are discussed, and it is shown that the spectrum of a class of Toeplitz operators defined on the Bergman spaceA 2 (D), is not connected. 相似文献
12.
Hua HE Chun Lan JIANG 《数学学报(英文版)》2005,21(6):1259-1268
In this paper, we are concerned with the classification of operators on complex separable Hilbert spaces, in the unitary equivalence sense and the similarity sense, respectively. We show that two strongly irreducible operators A and B are unitary equivalent if and only if W*(A+B)′≈M2(C), and two operators A and B in B1(Ω) are similar if and only if A′(AGB)/J≈M2(C). Moreover, we obtain V(H^∞(Ω,μ)≈N and Ko(H^∞(Ω,μ)≈Z by the technique of complex geometry, where Ω is a bounded connected open set in C, and μ is a completely non-reducing measure on Ω. 相似文献
13.
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
14.
José Giménez 《Integral Equations and Operator Theory》2002,43(4):385-396
We study joint hyponormality and joint subnormality of ofn-tuples of commuting composition operators with linear fractional symbols, acting on the Hardy spaceH
2. We also consider subnormality ofn-tuples of adjoints of composition operators. 相似文献
15.
We characterize the essentially normal composition operators induced on the Hardy space H2 by linear-fractional maps; they are either compact, normal, or (the nontrivial case) induced by parabolic nonautomorphisms. These parabolic maps induce the first known examples of nontrivially essentially normal composition operators. In addition, we characterize those linear-fractionally induced composition operators on H2 that are essentially self-adjoint, and present a number of results for composition operators induced by maps that are not linear-fractional. 相似文献
16.
Wolfram Bauer 《Journal of Functional Analysis》2009,256(10):3107-235
Extending results in [L.A. Coburn, The measure algebra of the Heisenberg group, J. Funct. Anal. 161 (1999) 509-525; L.A. Coburn, On the Berezin-Toeplitz calculus, Proc. Amer. Math. Soc. 129 (11) (2001) 3331-3338] we derive composition formulas for Berezin-Toeplitz operators with i.g. unbounded symbols in the range of certain integral transforms. The question whether a finite product of Berezin-Toeplitz operators is an operator of this type again can be answered affirmatively in several cases, but there are also well-known counter examples. We explain some consequences of such formulas to C∗-algebras generated by Toeplitz operators. 相似文献
17.
Anton Baranov 《Journal of Functional Analysis》2011,261(12):3437-3456
We consider three topics connected with coinvariant subspaces of the backward shift operator in Hardy spaces Hp:
- -
- properties of truncated Toeplitz operators;
- -
- Carleson-type embedding theorems for the coinvariant subspaces;
- -
- factorizations of pseudocontinuable functions from H1.
18.
We will consider the problem of which the products of composition and analytic Toeplitz operators would be bounded or compact on the Hardy space H2 and the Bergman space La2. 相似文献
19.
Brian C. Hall 《Journal of Functional Analysis》2008,255(9):2488-2506
Let K be a connected compact semisimple Lie group and KC its complexification. The generalized Segal-Bargmann space for KC is a space of square-integrable holomorphic functions on KC, with respect to a K-invariant heat kernel measure. This space is connected to the “Schrödinger” Hilbert space L2(K) by a unitary map, the generalized Segal-Bargmann transform. This paper considers certain natural operators on L2(K), namely multiplication operators and differential operators, conjugated by the generalized Segal-Bargmann transform. The main results show that the resulting operators on the generalized Segal-Bargmann space can be represented as Toeplitz operators. The symbols of these Toeplitz operators are expressed in terms of a certain subelliptic heat kernel on KC. I also examine some of the results from an infinite-dimensional point of view based on the work of L. Gross and P. Malliavin. 相似文献
20.
Gerard J. Murphy 《Integral Equations and Operator Theory》1992,15(5):825-852
Some aspects are developed of the theory of Toeplitz operators on generalised HardyH
2 spaces associated to function algebras. It is shown that a substantial number of results of the classical theory of Toeplitz operators on the circle extend to this situation, although counterexamples are given which show that there are also important differences. Spectral connectedness results are obtained, and a characterisation of invertibility for Toeplitz operators. The Fredholm theory is also studied. 相似文献