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1.
The paper is devoted to the study of specific properties of Toeplitz operators with (unbounded, in general) radial symbolsa=a(r). Boundedness and compactness conditions, as well as examples, are given. It turns out that there exist non-zero symbols which generate zero Toeplitz operators. We characterize such symbols, as well as the class of symbols for whichT
a
=0 impliesa(r)=0 a.e. For each compact setM there exists a Toeplitz operatorT
a
such that spT
a
=ess-spT
a
=M. We show that the set of symbols which generate bounded Toeplitz operators no longer forms an algebra under pointwise multiplication.Besides the algebra of Toeplitz operators we consider the algebra of Weyl pseudodifferential operators obtained from Toeplitz ones by means of the Bargmann transform. Rewriting our Toeplitz and Weyl pseudodifferential operators in terms of the Wick symbols we come to their spectral decompositions.This work was partially supported by CONACYT Project 27934-E, México.The first author acknowledges the RFFI Grant 98-01-01023, Russia. 相似文献
2.
N. L. Vasilevski 《Integral Equations and Operator Theory》1999,34(1):107-126
Let
be the unit disk in,
be the Bergman space, consisting of all analytic functions from
, and
be the Bergman projection of
onto
. We constructC
*-algebras
, for functions of which the commutator of Toeplitz operators [T
a
,T
b
]=T
a
T
b
–T
b
T
a
is compact, and, at the same time, the semi-commutator [T
a
,T
b
)=T
a
T
b
–T
ab
is not compact.It is proved, that for each finite set =n
0,n
1, ...,n
m
, where 1=n
0
1
<...
m
, andn
k
{}, there are algebras
of the above type, such that the symbol algebras Sym
of Toeplitz operator algebras
arecommutative, while the symbol algebras Sym
of the algebras
, generated by multiplication operators
and
, haveirreducible representations exactly of dimensions n
0,n
1,..., n
m
.This work was partially supported by CONACYT Project 3114P-E9607, México. 相似文献
3.
An operatorX:
is said to be a generalized Toeplitz operator with respect to given contractionsT
1 andT
2 ifX=T
2XT1
*. The purpose of this line of research, started by Douglas, Sz.-Nagy and Foia, and Pták and Vrbová, is to study which properties of classical Toeplitz operators depend on their characteristic relation. Following this spirit, we give appropriate extensions of a number of results about Toeplitz operators. Namely, Wintner's theorem of invertibility of analytic Toeplitz operators, Widom and Devinatz's invertibility criteria for Toeplitz operators with unitary symbols, Hartman and Wintner's theorem about Toeplitz operator having a Fredholm symbol, Hartman and Wintner's estimate of the norm of a compactly perturbed Toeplitz operator, and the non-existence of compact classical Toeplitz operators due to Brown and Halmos.Dedicated to our friend Cora Sadosky on the occasion of her sixtieth birthday 相似文献
4.
5.
Maribel Loaiza 《Integral Equations and Operator Theory》2005,51(1):141-153
Let
and
be a finite collection of smooth curves in D. Given k points
consider the family
of all bounded and continuous functions on
with finite limits at
and radial limits at zk. We study the Toeplitz operator algebra
corresponding to Mr and we prove that its Calkin algebra is isomorphic to the algebra of all continuous functions on some compact set. This fact implies that the commutator of two Toeplitz operators with this kind of symbols is compact. We also prove that the semi-commutator of such Toeplitz operators is not compact, in general. 相似文献
6.
Jie Miao 《Integral Equations and Operator Theory》1997,27(4):426-438
We study Toeplitz operators on the harmonic Bergman spaceb
p
(B), whereB is the open unit ball inR
n(n2), for 1<p. We give characterizations for the Toeplitz operators with positive symbols to be bounded, compact, and in Schatten classes. We also obtain a compactness criteria for the Toeplitz operators with continuous symbols. 相似文献
7.
In the case of radial symbols we study the behavior of different properties (boundedness, compactness, spectral properties, etc.) of Toeplitz operators Ta() acting on weighted Bergman spaces
over the unit disk
, in dependence on , and compare their limit behavior under
with corresponding properties of the initial symbol a. 相似文献
8.
Compact Hankel operators on harmonic Bergman spaces 总被引:2,自引:0,他引:2
Mirjana Jovović 《Integral Equations and Operator Theory》1995,22(3):295-304
We study Hankel operators on the harmonic Bergman spaceb
2(B), whereB is the open unit ball inR
n,n2. We show that iff is in
then the Hankel operator with symbolf is compact. For the proof we have to extend the definition of Hankel operators to the spacesb
p(B), 1<p<, and use an interpolation theorem. We also use the explicit formula for the orthogonal projection ofL
2(B, dV) ontob
2(B). This result implies that the commutator and semi-commutator of Toeplitz operators with symbols in
are compact. 相似文献
9.
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
10.
Ariyadasa Aluthge 《Integral Equations and Operator Theory》1996,24(4):497-501
A bounded linear operatorT is calledp-Hyponormal if (T
*T)p(TT
*)p, 0<p1. In Aluthge [1], we studied the properties of p-hyponormal operators using the operator
. In this work we consider a more general operator
, and generalize some properties of p-hyponormal operators obtained in [1]. 相似文献
11.
In this paper we show that the theory of Hankel operators in the torus
d
, ford>1, presents striking differences with that on the circle
, starting with bounded Hankel operators with no bounded symbols. Such differences are circumvented here by replacing the space of symbolsL
(
) by BMOr(
d
), a subspace of product BMO, and the singular numbers of Hankel operators by so-called sigma numbers. This leads to versions of the Nehari-AAK and Kronecker theorems, and provides conditions for the existence of solutions of product Pick problems through finite Picktype matrices. We give geometric and duality characterizations of BMOr, and of a subspace of it, bmo, closely linked withA
2 weights. This completes some aspects of the theory of BMO in product spaces.Sadosky was partially supported by NSF grants DMS-9205926, INT-9204043 and GER-9550373, and her visit to MSRI is supported by NSF grant DMS-9022140 to MSRI. 相似文献
12.
In 1997, V. Pták defined the notion of generalized Hankel operator as follows: Given two contractions
and
, an operatorX:
is said to be a generalized Hankel operator ifT
2
X=XT
1
*
andX satisfies a boundedness condition that depends on the unitary parts of the minimal isometric dilations ofT
1 andT
2. The purpose behind this kind of generalization is to study which properties of classical Hankel operators depend on their characteristic intertwining relation rather than on the theory of analytic functions. Following this spirit, we give appropriate versions of a number of results about compact and finite rank Hankel operators that hold within Pták's generalized framework. Namely, we extend Adamyan, Arov and Krein's estimates of the essential norm of a Hankel operator, Hartman's characterization of compact Hankel operators and Kronecker's characterization of finite rank Hankel operators.Dedicated to the memory of our master and friend Vlastimil Pták 相似文献
13.
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
14.
N. L. Vasilevski 《Integral Equations and Operator Theory》1998,31(1):113-132
We study the following problem: Given a Hilbert spaceH and a set of orthogonal projectionsP, Q
1, ..., Qn on it, with the conditionsQ
j
·Q
k
=
j,k
Q
k
,
, describe theC
*-algebraC
*(P, Q
1, ..., Qn) generated by these projections.Applications to Naimark dilation theorems and to Toeplitz operators associated with the Heisenberg group are given.Dedicated to the memory of M. G. Krein.This work was partially supported by CONACYT Project 3114P-E9608, México. 相似文献
15.
Marco Romito 《Monatshefte für Mathematik》1998,126(4):329-352
Given an open bounded convex subset of
p
, a strictly elliptic differential operatorL and a continuous function
, and denoted withT
L the Dirichlet operator associated withL, the Lototsky-Schnabl operators associated withT
L and are investigated. In particular, conditions are established which ensure the existence of a Feller semigroup represented by limit of powers of these operators. Then the analytic expression of the infinitesimal generator is determined and some properties of the semigroup are deduced. Finally, the saturation class of Lototsky-Schnabl operators is determined.Work supported by a C.N.R. Research Grant (n. 201.19.1, November 30, 1994) 相似文献
16.
For a Riesz operator T on a reflexive Banach space X with nonzero eigenvalues
denote by E(λi; T) the eigen-projection corresponding to an eigenvalue λi. In this paper we will show that if the operator sequence
is uniformly bounded, then the Riesz operator T can be decomposed into the sum of two operators Tp and Tr: T = Tp + Tr, where Tp is the weak limit of Tn and Tr is quasi-nilpotent. The result is used to obtain an expansion of a Riesz semigroup T(t) for t ≥ τ. As an application, we consider the solution of transport equation on a bounded convex body. 相似文献
17.
LetM be a von Neumann algebra with a faithful normal tracial state and letH
be a finite maximal subdiagonal subalgebra ofM. LetH
2 be the closure ofH
in the noncommutative Lebesgue spaceL
2(M). We consider Toeplitz operators onH
2 whose symbol belong toM, and find that they possess several of the properties of Toeplitz operators onH
2(
) with symbol fromL
(
), including norm estimates, a Hartman-Wintner spectral inclusion theorem, and a characterisation of the weak* continuous linear functionals on the space of Toeplitz operators. 相似文献
18.
In 1997 Ptak defined generalized Hankel operators as follows: Given two contractions
and
, an operator
is said to be a generalized Hankel operator if
and X satisfies a boundedness condition that depends on the unitary parts of the minimal isometric dilations of T
1 and T
2. This approach, call it (P), contrasts with a previous one developed by Ptak and Vrbova in 1988, call it (PV), based on the existence of a previously defined generalized Toeplitz operator. There seemed to be a strong but somewhat hidden connection between the theories (P) and (PV) and we clarify that connection by proving that (P) is more general than (PV), even strictly more general for some T
1 and T
2, and by studying when they coincide. Then we characterize the existence of Hankel operators, Hankel symbols and analytic Hankel symbols, solving in this way some open problems proposed by Ptak. 相似文献
19.
Atsushi Uchiyama 《Integral Equations and Operator Theory》1999,33(2):221-230
For an-multicyclicp-hyponormal operatorT, we shall show that |T|2p
–|T
*|2p
belongs to the Schatten
and that tr
Area ((T)). 相似文献
20.
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