共查询到20条相似文献,搜索用时 15 毫秒
1.
In this paper, we study the boundedness and the compactness of composition operators on Orlicz–Lorentz spaces.
相似文献
2.
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
3.
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
4.
Linear-Fractional Composition Operators in Several Variables 总被引:1,自引:0,他引:1
We investigate properties of linear-fractional composition operators Cφ on Hardy and Bergman spaces of the ball in
that are motivated by a formula for the self-commutator [Cφ* ,Cφ]. In particular, we characterize when certain commutators [Cφ, Cσ] are compact, and give conditions under which
is compact, where
is multiplication by the monomial zβ. Our results allow us to determine when Cφ is essentially normal, for φ belonging to a large class of linear-fractional symbols. 相似文献
5.
Takuya Hosokawa Keiji Izuchi Shûichi Ohno 《Integral Equations and Operator Theory》2005,53(4):509-526
We study properties of the topological space of weighted composition operators on the space of bounded analytic functions
on the open unit disk in the uniform operator topology. Moreover, we characterize the compactness of differences of two weighted
composition operators. 相似文献
6.
Frédéric Bayart 《Monatshefte für Mathematik》2002,136(3):203-236
In [9], Hedenmalm, Lindqvist and Seip introduce the Hilbert space of Dirichlet series with square summable coefficients , and begin its study, with modern functional and harmonic analysis tools. The space is an analogue for Dirichlet series of the space for Fourier series. We continue their study by introducing , an analogue to the spaces . Thanks to Bohr’s vision of Dirichlet series, we identify with the Hardy space of the infinite polydisk . Next, we study a variant of the Poisson semigroup for Dirichlet series. We give a result similar to the one of Weissler
([25]) about the hypercontractivity of this semigroup on the spaces . Finally, following [8], we determine the composition operators on , and we compare some properties of such an operator and of its symbol.
Received October 3, 2001; in revised form January 16, 2002 Published online July 12, 2002 相似文献
7.
Essential Norms of Composition Operators 总被引:2,自引:0,他引:2
We obtain simple estimates for the essential norm of a composition
operator acting from the Hardy space H
p
to H
q
, p > q, in one or several
variables. When p = and q = 2 our results give an exact formula for the
essential norm. 相似文献
8.
Valentin Matache 《Complex Analysis and Operator Theory》2008,2(1):169-197
Operators on function spaces acting by composition to the right with a fixed selfmap φ of some set are called composition operators of symbol φ. A weighted composition operator is an operator equal to a composition operator followed by a multiplication operator. We
summarize the basic properties of bounded and compact weighted composition operators on the Hilbert Hardy space on the open
unit disk and use them to study composition operators on Hardy–Smirnov spaces.
Submitted: January 30, 2007. Revised: June 19, 2007. Accepted: July 11, 2007. 相似文献
9.
Jussi Laitila 《Integral Equations and Operator Theory》2007,58(4):487-502
Analytic composition operators
are studied on X-valued versions of BMOA, the space of analytic functions on the unit disk that have bounded mean oscillation on the unit
circle, where X is a complex Banach space. It is shown that if X is reflexive and C
φ is compact on BMOA, then C
φ is weakly compact on the X-valued space BMOA
C
(X) defined in terms of Carleson measures. A related function-theoretic characterization is given of the compact composition
operators on BMOA. 相似文献
10.
J. S. Manhas 《Integral Equations and Operator Theory》2008,62(3):419-428
Let be the weighted Banach space of analytic functions with a topology generated by weighted sup-norm. In the present article,
we investigate the analytic mappings and which characterize the compactness of differences of two weighted composition operators on the space . As a consequence we characterize the compactness of differences of composition operators on weighted Bloch spaces.
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11.
Dana D. Clahane 《Integral Equations and Operator Theory》2005,51(1):41-56
Let H2(D) denote the Hardy space of a bounded symmetric domain
in its standard Harish-Chandra realization, and let
be the weighted Bergman space with
and
where
is a critical value depending on D. Suppose that
is holomorphic. We show that if the composition operator
defined by
is compact (or, more generally, power-compact) on H2(D) or
then has a unique fixed point z0 in D. We then prove that the spectrum of
as an operator on these function spaces is precisely the set consisting of 0, 1, and all possible products of eigenvalues of
These results extend previous work by Caughran/Schwartz and MacCluer. As a corollary, we now have that MacCluers previous spectrum results on the unit ball Bn extend to Hp(n) (not only for p = 2 but for all p > 1) and
(for p 1), where n is the polydisk in
相似文献
12.
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
13.
James E. Jamison 《Integral Equations and Operator Theory》2006,56(4):469-482
A pair of operators on a Banach space X are isometrically equivalent if they are intertwined by a surjective isometry of X. We investigate the isometric equivalence problem for pairs of operators on specific types of Banach spaces. We study weighted
shifts on symmetric sequence spaces, elementary operators acting on an ideal I of Hilbert space operators, and composition operators on the Bloch space. This last case requires an extension of known results
about surjective isometries of the Bloch space. 相似文献
14.
Thomas E. Goebeler Jr. 《Integral Equations and Operator Theory》2001,41(4):389-395
A function-theoretic necessary and sufficient condition on a symbol is given for the compactness of the induced composition operator acting betweenH
p
andH
q
, forq
. Compact differences of such composition operators are shown to occur only in the trivial case of both operators being compact themselves. 相似文献
15.
Olivia Constantin 《Integral Equations and Operator Theory》2007,59(4):523-554
We prove a general atomic decomposition theorem for weighted vector-valued Bergman spaces, which applies to duality problems
and to the study of compact Toeplitz type operators.
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16.
Marian E. Robbins 《Integral Equations and Operator Theory》2002,43(4):480-487
Given a large weighted Hardy space we show there exists a composition operatorC
with that maps from that space into the unweighted Dirichlet space and lies in every Schatten p-class for 0<p<. This is in contrast to the situation in which the image space is a smaller weighted Dirichlet space. It is known that in that case it is not possible to find such a composition operator that is bounded.This research was supported in part by a summer stipend from Bellarmine College. 相似文献
17.
Wolfgang Arendt 《Positivity》2008,12(1):25-44
Extending results of Davies and of Keicher on ℓp we show that the peripheral point spectrum of the generator of a positive bounded C0-semigroup of kernel operators on Lp is reduced to 0. It is shown that this implies convergence to an equilibrium if the semigroup is also irreducible and the
fixed space non-trivial. The results are applied to elliptic operators.
Dedicated to the memory of H.H. Schaefer 相似文献
18.
Complementing and generalizing classical as well as recent results, we prove asymptotically optimal formulas for the Gelfand
and approximation numbers of identities En ↪ Fn, where En and Fn denote the n-th sections of symmetric quasi-Banach
sequence spaces E and F satisfying certain interpolation assumptions. We illustrate our
results by considering classical spaces such as Lorentz and Orlicz sequence spaces.
Supported by DFG grant Hi 584/2-2. 相似文献
19.
20.
This paper characterizes the component structure of the space of
composition operators acting on
, both in the operator norm topology
and in the topology induced by the essential norm. 相似文献