共查询到20条相似文献,搜索用时 15 毫秒
1.
Miroslav Engliš 《Arkiv f?r Matematik》1992,30(1-2):227-243
In this paper it is shown that Toeplitz operators on Bergman space form a dense subset of the space of all bounded linear operators, in the strong operator topology, and that their norm closure contains all compact operators. Further, theC *-algebra generated by them does not contain all bounded operators, since all Toeplitz operators belong to the essential commutant of certain shift. The result holds in Bergman spacesA 2(Ω) for a wide class of plane domains Ω?C, and in Fock spacesA 2(C N),N≧1. 相似文献
2.
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
3.
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
4.
Norma Elias 《Integral Equations and Operator Theory》1988,11(3):310-331
In [2], Axler, Conway and McDonald, discuss the essential spectrum of Toeplitz operator, with continuous symbol, on the unweighted Bergman space. This paper extends their results to the weighted Bergman space, where the weight and its logarithm are assumed to be locally integrable.This paper represents part of the author's Ph.D. thesis, written at Indiana University under the direction of Professor John B. Conway. 相似文献
5.
6.
Chunlan Jiang 《Journal of Functional Analysis》2010,258(9):2961-2982
In this paper we give a function theoretic similarity classification for Toeplitz operators on weighted Bergman spaces with symbol analytic on the closure of the unit disk. 相似文献
7.
Czechoslovak Mathematical Journal - We study algebraic properties of two Toeplitz operators on the weighted Bergman space on the unit disk with harmonic symbols. In particular the product property... 相似文献
8.
Eun Sun Choi 《Journal of Mathematical Analysis and Applications》2007,327(1):679-694
Recently, Schatten-Herz type Toeplitz operators have been studied on the Bergman spaces and the harmonic Bergman spaces. Motivated these results, we study characterizations of positive Toeplitz operators of Schatten-Herz type in terms of averaging functions and Berezin transforms of symbol functions on the ball of pluriharmonic Bergman spaces. 相似文献
9.
For an operator which is a finite sum of products of finitely many Toeplitz operators on the harmonic Bergman space over the half-space, we study the problem: Does the boundary vanishing property of the Berezin transform imply compactness? This is motivated by the Axler-Zheng theorem for analytic Bergman spaces, but the answer would not be yes in general, because the Berezin transform annihilates the commutator of any pair of Toeplitz operators. Nevertheless we show that the answer is yes for certain subclasses of operators. In order to do so, we first find a sufficient condition on general operators and use it to reduce the problem to whether the Berezin transform is one-to-one on related subclasses. 相似文献
10.
Eun Sun Choi 《Czechoslovak Mathematical Journal》2008,58(1):93-111
We study Toeplitz operators between the pluriharmonic Bergman spaces for positive symbols on the ball. We give characterizations
of bounded and compact Toeplitz operators taking a pluriharmonic Bergman space b
p
into another b
q
for 1 < p, q < ∞ in terms of certain Carleson and vanishing Carleson measures.
This research was supported by KOSEF (R01-2003-000-10243-0) and Korea University Grant. 相似文献
11.
12.
We find a concrete integral formula for the class of generalized Toeplitz operators \(T_a\) in Bergman spaces \(A^p\), \(1<p<\infty \), studied in an earlier work by the authors. The result is extended to little Hankel operators. We give an example of an \(L^2\)-symbol a such that \(T_{|a|} \) fails to be bounded in \(A^2\), although \(T_a : A^2 \rightarrow A^2\) is seen to be bounded by using the generalized definition. We also confirm that the generalized definition coincides with the classical one whenever the latter makes sense. 相似文献
13.
14.
In this note we construct a function φ in L2(Bn,dμ) which is unbounded on any neighborhood of each boundary point of Bn such that Tφ is a trace class operator on weighted Bergman space Lα2(Bn,dμ) for several complex variables. 相似文献
15.
It is proved that the operator Lie algebra ε(T,T∗) generated by a bounded linear operator T on Hilbert space H is finite-dimensional if and only if T=N+Q, N is a normal operator, [N,Q]=0, and dimA(Q,Q∗)<+∞, where ε(T,T∗) denotes the smallest Lie algebra containing T,T∗, and A(Q,Q∗) denotes the associative subalgebra of B(H) generated by Q,Q∗. Moreover, we also give a sufficient and necessary condition for operators to generate finite-dimensional semi-simple Lie algebras. Finally, we prove that if ε(T,T∗) is an ad-compact E-solvable Lie algebra, then T is a normal operator. 相似文献
16.
In this paper, we study the commutativity of dual Toeplitz operators on weighted Bergman spaces of the unit ball. We obtain
the necessary and sufficient conditions for the commutativity, essential commutativity and essential semi-commutativity of
dual Toeplitz operator on the weighted Bergman spaces of the unit ball. 相似文献
17.
Congwen Liu 《Proceedings of the American Mathematical Society》2007,135(9):2867-2876
Let denote the open unit ball in for and the Lebesgue volume measure on . For , the (weighted) harmonic Bergman space is the space of all harmonic functions which are in . For , the Toeplitz operator is defined on by , where is the orthogonal projection of onto . In this note, we prove that for radial, .
18.
Toeplitz operators and algebras 总被引:3,自引:0,他引:3
G. J. Murphy 《Mathematische Zeitschrift》1991,208(1):355-362
19.
Renata Otá halová 《Proceedings of the American Mathematical Society》2008,136(7):2483-2492
For the standard weighted Bergman spaces on the complex unit ball, the Berezin transform of a bounded continuous function tends to this function pointwise as the weight parameter tends to infinity. We show that this remains valid also in the context of harmonic Bergman spaces on the real unit ball of any dimension. This generalizes the recent result of C. Liu for the unit disc, as well as the original assertion concerning the holomorphic case. Along the way, we also obtain a formula for the corresponding weighted harmonic Bergman kernels.