共查询到20条相似文献,搜索用时 12 毫秒
1.
Pascal Lefèvre 《Integral Equations and Operator Theory》2009,63(4):557-569
We compute the essential norm of a composition operator relatively to the class of Dunford-Pettis operators or weakly compact
operators, on some uniform algebras of analytic functions. Even in the context of H∞ (resp. the disk algebra), this is new, as well for the polydisk algebras and the polyball algebras. This is a consequence
of a general study of weighted composition operators.
相似文献
2.
We study composition operators on the space of bounded harmonic functions on the open unit disk. The principal goal of this
paper is to provide criteria for determining the essential norm of difference of two composition operators.
The third author is partially supported by Grant-in-Aid for Scientific Research (No.17540169), Japan Society for the Promotion
of Science. 相似文献
3.
O. Blasco M. D. Contreras S. Díaz-Madrigal J. Martínez A. G. Siskakis 《Integral Equations and Operator Theory》2008,61(1):45-62
In this paper we deal with the maximal subspace in BMOA where a general semigroup of analytic functions on the unit disk generates a strongly continuous semigroup of composition
operators. Particular cases of this question are related to a well-known theorem of Sarason about VMOA. Our results describe analytically that maximal subspace and provide a condition which is sufficient for the maximal subspace
to be exactly VMOA. A related necessary condition is also proved in the case when the semigroup has an inner Denjoy-Wolff point. As a byproduct
we provide a generalization of the theorem of Sarason.
This research has been partially supported by the Ministerio de Educación y Ciencia projects n. MTM2006-14449-C02-01 and MTM2005-08350-C03-03 and by La Consejería de Educación y Ciencia de la Junta de Andalucía. 相似文献
4.
On the setting of the half-space we introduce the Schatten-Herz classes of Toeplitz operators and obtain characterizations
for positive Toeplitz operators to belong to those classes. We also prove results concerning the boundedness and compactness
of Toeplitz operators with Herz symbols. Such a study has been recently done on the ball. At a critical step of the proofs
we employ a much simplified argument to extend the range of parameters for Herz spaces on which the Berezin transform is bounded.
Our results show not only that most of results on the ball continue to hold, but also that there is some pathology caused
by the unboundedness of the domain.
The first author was in part supported by a Korea University Grant(2007), the second author was in part supported by Hanshin
University Research Grant, and both authors were in part supported by KOSEF(R01-2003-000-10243-0). 相似文献
5.
Elena Litsyn 《Integral Equations and Operator Theory》2007,58(2):239-253
The new definition of Volterra operator introduced in [5] allows specification of the classical theory of linear equations
in Banach spaces to equations with such operators. Here we specially address relations between properties of the given linear
equation with Volterra operator and properties of its conjugate. As well we treat the theory of Noetherian and Fredholm equations. 相似文献
6.
Amol Sasane 《Complex Analysis and Operator Theory》2009,3(1):323-330
Let E be a separable infinite-dimensional Hilbert space, and let denote the algebra of all functions that are holomorphic. If is a subalgebra of , then using an algebraic result of Corach and Larotonda, we derive that under some conditions, the Bass stable rank of is infinite. In particular, we deduce that the Bass (and hence topological stable ranks) of the Hardy algebra , the disk algebra and the Wiener algebra are all infinite.
Submitted: October 10, 2007., Revised: January 11, 2008., Accepted: January 12, 2007. 相似文献
7.
In this paper, we study the boundedness and the compactness of composition operators on Orlicz–Lorentz spaces.
相似文献
8.
We define Toeplitz operators on all Dirichlet spaces on the unit ball of
and develop their basic properties. We characterize bounded, compact, and Schatten-class Toeplitz operators with positive
symbols in terms of Carleson measures and Berezin transforms. Our results naturally extend those known for weighted Bergman
spaces, a special case applies to the Arveson space, and we recover the classical Hardy-space Toeplitz operators in a limiting
case; thus we unify the theory of Toeplitz operators on all these spaces. We apply our operators to a characterization of
bounded, compact, and Schatten-class weighted composition operators on weighted Bergman spaces of the ball. We lastly investigate
some connections between Toeplitz and shift operators.
The research of the second author is partially supported by a Fulbright grant. 相似文献
9.
Benoit Florent Sehba 《Integral Equations and Operator Theory》2008,62(2):233-245
We present here some criteria for Schatten-Von Neumann class membership for the small Hankel operator on Bergman space A
2(T
Ω), when T
Ω is the tube over the symmetric cone Ω.
The author would like to thank professor Aline Bonami for helpful advices. 相似文献
10.
Manuel D. Contreras Alfredo G. Hernández-Díaz 《Integral Equations and Operator Theory》2003,46(2):165-188
Let and be two analytic functions defined on such that. The operator given by is called a weighted composition
operator. In this paper we deal with the boundedness, compactness,
weak compactness, and complete continuity of weighted composition operators
from a Hardy space H
p
into another Hardy space H
q
.
We apply these results to study composition operators on Hardy spaces of a
half-plane.
Submitted: November 20, 2001. 相似文献
11.
Extremal Problems for Operators in Banach Spaces Arising in the Study of Linear Operator Pencils, II
M. I. Ostrovskii 《Integral Equations and Operator Theory》2005,51(4):553-564
This paper is devoted to the study of operators satisfying the condition
where stands for the spectral radius; and Banach spaces in which all operators satisfy this condition. Such spaces are called V–spaces. The present paper contains partial solutions of some of the open problems posed in the first part of the paper. The main results: (1) Each subspace of lp (1 < p < ) is a V–space. (2) For each infinite dimensional Banach space X there exists an equivalent norm |||·||| on X such that the space (X, |||·|||) is not a V–space. (3) Let X be a separable infinite dimensional Banach space with a symmetric basis. If X has the V-property, then X is isometric to lp, 1 < p < . 相似文献
12.
We show that if a small holomorphic Sobolev space on the unit disk is not just small but very small, then a trivial necessary
condition is also sufficient for a composition operator to be bounded. A similar result for holomorphic Lipschitz spaces is
also obtained. These results may be viewed as boundedness analogues of Shapiro’s theorem concerning compact composition operators
on small spaces. We also prove the converse of Shapiro’s theorem if the symbol function is already contained in the space
under consideration. In the course of the proofs we characterize the bounded composition operators on the Zygmund class. Also,
as a by-product of our arguments, we show that small holomorphic Sobolev spaces are algebras. 相似文献
13.
Kyunguk Na 《Integral Equations and Operator Theory》2009,64(3):409-428
We study characterizations of arbitrary positive Toeplitz operators of Schatten (or Schatten-Herz) type in terms of averaging
functions and Berezin transforms of symbol functions on the ball of pluriharmonic Bergman space.
This work was supported by a Hanshin University Research Grant. 相似文献
14.
Let A
0, ... , A
n−1 be operators on a separable complex Hilbert space , and let α0,..., α
n−1 be positive real numbers such that 1. We prove that for every unitarily invariant norm,
for 2 ≤ p < ∞, and the reverse inequality holds for 0 < p ≤ 2. Moreover, we prove that if ω0,..., ω
n−1 are the n roots of unity with ω
j
= e
2πij/n
, 0 ≤ j ≤ n − 1, then for every unitarily invariant norm,
for 2 ≤ p < ∞, and the reverse inequalities hold for 0 < p ≤ 2. These inequalities, which involve n-tuples of operators, lead to natural generalizations and refinements of some of the classical Clarkson inequalities in the
Schatten p-norms. Extensions of these inequalities to certain convex and concave functions, including the power functions, are olso
optained.
相似文献
15.
Differences of Composition Operators between Weighted Banach Spaces of Holomorphic Functions on the Unit Polydisk 总被引:1,自引:0,他引:1
Elke Wolf 《Results in Mathematics》2008,51(3-4):361-372
We consider differences of composition operators between given weighted Banach spaces H
∞
v
or H
0
v
of analytic functions defined on the unit polydisk D
N
with weighted sup-norms and give estimates for the distance of these differences to the space of compact operators. We also
study boundedness and compactness of the operators. This paper is an extension of [6] where the one-dimensional case is treated.
Received: May 15, 2007. Revised: October 8, 2007. 相似文献
16.
Fredholm criteria and index formulas are established for Wiener-Hopf operators W(a) with semi-almost periodic matrix symbols a on weighted Lebesgue spaces where 1 < p < ∞, w belongs to a subclass of Muckenhoupt weights and . We also study the invertibility of Wiener-Hopf operators with almost periodic matrix symbols on . In the case N = 1 we also obtain a semi-Fredholm criterion for Wiener-Hopf operators with semi-almost periodic symbols and, for another
subclass of weights, a Fredholm criterion for Wiener-Hopf operators with semi-periodic symbols.
Work was supported by the SEP-CONACYT Project No. 25564 (México). The second author was also sponsored by the CONACYT scholarship
No. 163480. 相似文献
17.
Bebe Prunaru 《Integral Equations and Operator Theory》2008,61(1):121-145
In this paper we establish a connection between the approximate factorization property appearing in the theory of dual algebras
and the spectral inclusion property for a class of Toeplitz operators on Hilbert spaces of vector valued square integrable
functions. As an application, it follows that a wide range of dual algebras of subnormal Toeplitz operators on various Hardy
spaces associated to function algebras have property (A
1(1)). It is also proved that the dual algebra generated by a spherical isometry (with a possibly infinite number of components)
has the same property. One particular application is given to the existence of unimodular functions sitting in cyclic invariant
subspaces of weak* Dirichlet algebras. Moreover, by this method we provide a unified approach to several Toeplitz spectral
inclusion theorems.
Research partially supported by grant CNCSIS GR202/2006 (cod 813). 相似文献
18.
Interpretation, derivation and application of a variation of constants formula for measure-valued functions motivate our investigation
of properties of particular Banach spaces of Lipschitz functions on a metric space and semigroups defined on their (pre)duals.
Spaces of measures densely embed into these preduals. The metric space embeds continuously in these preduals, even isometrically
in a specific case. Under mild conditions, a semigroup of Lipschitz transformations on the metric space then embeds into a
strongly continuous semigroups of positive linear operators on these Banach spaces generated by measures.
相似文献
19.
Dr. Mohammed Hichem Mortad 《Integral Equations and Operator Theory》2009,64(3):399-408
We give a spectral analysis of some unbounded normal product HK of two self-adjoint operators H and K (which appeared in [7]) and we say why it is not self-adjoint even if the spectrum of one of the operators is sufficiently
“asymmetric”. Then, we investigate the self-adjointness of KH (given it is normal) for arbitrary self-adjoint H and K by giving a counterexample and some positive results and hence finishing off with the whole question of normal products of
self-adjoint operators (appearing in [1, 7, 12]).
The author was supported in part by CNEPRU: B01820070020 (Ministry of Higher Education, Algeria). 相似文献
20.
Roberto C. Raimondo 《Integral Equations and Operator Theory》2007,57(3):425-449
In this paper we study the problem of the membership of H
ϕ in the Hilbert-Schmidt class, when
and Ω is a planar domain. We find a necessary and sufficient condition.We apply this result to the problem of joint membership
of H
φ and
in the Hilbert-Schmidt class. Using the notion of Berezin Transform and a result of K. Zhu we are able to give a necessary
and sufficient condition. Finally, we recover a result of Arazy, Fisher and Peetre on the case
with φ holomorphic. 相似文献