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1.
We study the commuting problem for Toeplitz operators on the harmonic Bergman space of the unit disk. We show that an analytic Toeplitz operator and a co-analytic Toeplitz operator with certain noncyclicity hypothesis can commute only when one of their symbols is constant. We also obtain analogous results for semi-commutants. 相似文献
2.
Motivated by recent works of Ahern and uković on the disk, we study the generalized zero product problem for Toeplitz operators acting on the Bergman space of the polydisk. First, we extend the results to the polydisk. Next, we study the generalized compact product problem. Our results are new even on the disk. As a consequence on higher dimensional polydisks, we show that the generalized zero and compact product properties are the same for Toeplitz operators in a certain case.The first three authors were partially supported by KOSEF(R01-2003-000-10243-0) and the last author was partially supported by the National Science Foundation. 相似文献
3.
Extending known results for the unit disk, we prove that for the unit ball there exist n+2 different cases of commutative C*-algebras generated by Toeplitz operators, acting on weighted Bergman spaces. In all cases the bounded measurable symbols
of Toeplitz operators are invariant under the action of certain commutative subgroups of biholomorphisms of the unit ball.
This work was partially supported by CONACYT Projects 46936 and 44620, México. 相似文献
4.
On Toeplitz operators with quasihomogeneous symbols 总被引:2,自引:0,他引:2
In this paper, we give some basic results concerning Toeplitz operators whose symbol is of the form ei p θϕ, where ϕ is a radial function, then use these results to characterize all Toeplitz operators which commute with them.Received: 12 June 2004; revised: 27 January 2005 相似文献
5.
Jong-Do Park 《Integral Equations and Operator Theory》2006,54(4):571-584
We investigate necessary and sufficient conditions for boundedness of the operator
on the Bergman space of the unit ball
for n ≥ 1, where Tf is the Toeplitz operator. Those conditions are related to boundedness of the Berezin transform of symbols f and g. We construct the inner product formula which plays a crucial role in proving the sufficiency of the conditions. 相似文献
6.
Semi-commutators of Toeplitz operators on the Bergman space 总被引:3,自引:0,他引:3
Dechao Zheng 《Integral Equations and Operator Theory》1996,25(3):347-372
In this paper several necessary and sufficient conditions are obtained for the semi-commutator
of Toeplitz operators
andT
g
with bounded pluriharmonic symbols on the unit ball to be compact on the Bergman space. Using
-harmonic function theory on the unit ball we show that
with bounded pluriharmonic symbolsf andg is zero on the Bergman space of the unit ball or the Hardy space of the unit sphere if and only if eitherf org is holomorphic.The author was supported in part by the National Science Foundation. 相似文献
7.
A well known lemma attributed to Coburn states that a Toeplitz operator with non-trivial kernel acting on the Hardy space must have dense range. We show that the range of a non-zero Toeplitz operator with non-trivial kernel must contain all polynomials and state this in a precise form. 相似文献
8.
We characterize complex measures μ on the unit disk for which the Toeplitz operator T
μ
is bounded or compact on the analytic Besov spaces B
p
with 1 ≤ p < ∞.
Research supported in part by NSF grant, DMS 0200587 (first author); and by a NSERC grant (third author). 相似文献
9.
A. Rogozhin 《Integral Equations and Operator Theory》2007,57(2):283-301
In this paper we estimate the norm of the Moore-Penrose inverse T(a)+ of a Fredholm Toeplitz operator T(a) with a matrix-valued symbol a∈LN × N∞ defined on the complex unit circle. In particular, we show that in the ”generic case” the strict inequality ||T(a)+|| > ||a−1||∞ holds. Moreover, we discuss the asymptotic behavior of ||T(tra)+|| for
. The results are illustrated by numerical experiments. 相似文献
10.
Compact Operators on Bergman Spaces 总被引:2,自引:0,他引:2
We prove that a bounded operator S on L
a
p
for p > 1 is compact if
and only if the Berezin transform of S vanishes on the boundary of the unit
disk if S satisfies some integrable conditions. Some estimates about the norm
and essential norm of Toeplitz operators with symbols in BT are obtained. 相似文献
11.
N.L. Vasilevski 《Integral Equations and Operator Theory》2003,46(2):235-251
We exhibit a surprising but natural connection among the Bergman
space structure, commutative algebras of Toeplitz operators and pencils of
hyperbolic straight lines. The commutative C*-algebras of Toeplitz operators
on the unit disk can be classified as follows. Each pencil of hyperbolic straight
lines determines the set of symbols consisting of functions which are constant
on corresponding cycles, the orthogonal trajectories to lines forming a pencil.
It turns out that the C*-algebra generated by Toeplitz operators with this
class of symbols is commutative.
Submitted: January 15, 2001?Revised: February 7, 2002 相似文献
12.
Maribel Loaiza Marcos López-García Salvador Pérez-Esteva 《Integral Equations and Operator Theory》2005,53(2):287-296
In this paper we decompose
into diadic annuli
and consider the class Sp,q of Toeplitz operators Tφ for which the sequence of Schatten norms
belongs to ℓq, where φn = φχ An. We study the boundedness and compactness of the operators in Sp,q and we describe the operators Tφ , φ ≥ 0 in these spaces in terms of weighted Herz norms of the averaging operator of the symbols φ. 相似文献
13.
For an invariant subspace I of the Bergman space
on the unit disk D, the associated inner space I zI has been known to have nice properties K. Zhu has recently given, in terms of kernels of Hankel operators, several characterizations for an inner space to be maximal. We show that maximality of inner spaces can be understood alternatively by use of the adjoint operator of the Bergman shift operator on
相似文献
14.
It is known that for particular classes of operators on certain reproducing
kernel Hilbert spaces, key properties of the operators (such as boundedness
or compactness) may be determined by the behaviour of the operators
on the reproducing kernels. We prove such results for Toeplitz operators on
the Paley-Wiener space, a reproducing kernel Hilbert space over
. Namely,
we show that the norm of such an operator is equivalent to the supremum of
the norms of the images of the normalised reproducing kernels of the space.
In particular, therefore, the operator is bounded exactly when this supremum
is finite. In addition, a counterexample is provided which shows that the operator
norm is not equivalent to the supremum of the norms of the images
of the real normalised reproducing kernels. We also give a necessary and
sufficient condition for compactness of the operators, in terms of their limiting
behaviour on the reproducing kernels. 相似文献
15.
Željko Čučković 《Integral Equations and Operator Theory》2007,59(3):345-353
We study finite rank perturbations of the Brown-Halmos type results involving products of Toeplitz operators acting on the
Bergman space.
相似文献
16.
Gerard J. Murphy 《Integral Equations and Operator Theory》1992,15(1):72-81
We consider the question of when a Toeplitz operator with continuous symbol on a connected compact abelian group is almost invertible, and show that this occurs precisely when the symbol is invertible and has zero topological index. The proof uses someK-theory computations. 相似文献
17.
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
18.
S. Asserda 《Integral Equations and Operator Theory》2006,55(1):1-18
Let
denote the closed subspace of
consisting of analytic functions in the unit disc
. For certain class of subharmonic functions
and
, it is shown that the essential norm of Hankel operator
is comparable to the distance norm from Hf to compact Hankel operators. 相似文献
19.
Congquan Yan 《Integral Equations and Operator Theory》2006,56(4):587-595
In this paper, we obtain a Fredholm index formula for Toeplitz operators whose symbols are certain piecewise continuous function
matrices on the unit ball. Moreover, using this formula, we discuss the automorphisms on the corresponding Toeplitz algebra 相似文献
20.
Algebraic Properties of Toeplitz Operators with Radial Symbols on the Bergman Space of the Unit Ball
In this paper, we discuss some algebraic properties of Toeplitz operators with radial symbols on the Bergman space of the
unit ball in . We first determine when the product of two Toeplitz operators with radial symbols is a Toeplitz operator. Next, we investigate
the zero-product problem for several Toeplitz operators with radial symbols. Also, the corresponding commuting problem of
Toeplitz operators whose symbols are of the form is studied, where and φ is a radial function.
Ze-Hua Zhou: supported in part by the National Natural Science Foundation of China (Grand Nos.10671141, 10371091). 相似文献