共查询到20条相似文献,搜索用时 15 毫秒
1.
We provide an alternate approach to an intertwining lifting theorem obtained by Ball, Trent and Vinnikov. The results are an exact analogue of the classical Sz-Nagy-Foias theorem in the case of multipliers on a class of reproducing kernel spaces, which satisfy the Nevanlinna-Pick property. 相似文献
2.
This paper mainly concerns the essential normality of graded submodules. Essentially all of the basic Hilbert modules that
have received attention over the years are p-essentially normal—including the d-shift Hilbert module, the Hardy and Bergman modules of the unit ball. Arveson conjectured graded submodules over the unit
ball inherit this property and provided motivations to seek an affirmative answer. Some positive results have been obtained
by Arveson and Douglas. However, the problem has been resistant. In dimensions d = 2, 3, this paper shows that the Arveson’s conjecture is true. In any dimension, the paper also gives an affirmative answer
in the case of the graded principal submodule. Finally, the paper is associated with K-homology invariants arising from graded quotient modules, by which geometry of the quotient modules and geometry of algebraic
varieties are connected. In dimensions d = 2, 3, it is shown that K-homology invariants determined by graded quotients are nontrivial. The paper also establishes results on p-smoothness of K-homology elements, and gives an explicit expression for K-homology invariant in dimension d = 2. 相似文献
3.
Kunyu Guo 《Journal of Functional Analysis》2004,213(2):380-411
This paper mainly concerns defect operators and defect functions of Hardy submodules, Bergman submodules over the unit ball, and Hardy submodules over the polydisk. The defect operator (function) carries key information about operator theory (function theory) and structure of analytic submodules. The problem when a submodule has finite defect is attacked for both Hardy submodules and Bergman submodules. Our interest will be in submodules generated by polynomials. The reason for choosing such submodules is to understand the interaction of operator theory, function theory and algebraic geometry. 相似文献
4.
Yongjiang Duan 《Integral Equations and Operator Theory》2007,58(3):301-314
This paper is to study the quasihomogeneous Hilbert modules and generalize a result of Arveson [3] which relates the curvature
invariant to the index of the Dirac operator.
This work was partially supported by NKBRPC (#2006CB805905) and SRFDP. 相似文献
5.
It is well known that the Hilbert matrix operator H is a bounded operator from the Bergman space into if and only if . In [5] it was shown that the norm of the Hilbert matrix operator H on the Bergman space is equal to , when , and it was also conjectured that when . In this paper we prove this conjecture. 相似文献
6.
We consider Hilbert spaces
of analytic functions defined on an open subset
of
, stable under the operator Mu of multiplication by some function u. Given a subspace
of
which is nearly invariant under division by u, we provide a factorization linking each element of
to elements of
on the inverse image under u of a certain complex disc, for which we give a relatively simple formula. By applying these results to
and u(z) = z, we obtain interesting results involving a H2-norm control. In particular, we deduce a factorization for the kernel of Toeplitz operators on Dirichlet spaces. Finally, we give a localization for the problem of extraneous zeros.Submitted: January 18, 2003 Revised: December 20, 2003 相似文献
7.
8.
J. F. Brasche 《Potential Analysis》1995,4(3):297-307
We present the first steps towards a general extension theory inL
2-spaces. By this theory it is possible to construct all perturbations of the Laplacian supported by a closed setN even if the classical capacity ofN equals zero. 相似文献
9.
10.
11.
Associated with a boundedg-holed (g0) planar domainD are two types of reproducing kernel Hilbert spaces of meromorphic functions onD. We give explicit formulas for the reproducing kernel functions of these spaces. The formulas are in terms of theta functions defined on the Jacobian variety of the Schottky double of the regionD. As applications we settle a conjecture of Abrahamse concerning Nevalinna-Pick interpolation on an annulus and obtain explicit formulas for the curvature (in the sense of Cowen and Douglas) of rank 1 bundle shift operators. 相似文献
12.
Omar Hirzallah 《Linear algebra and its applications》2007,424(1):71-82
We prove several singular value inequalities and norm inequalities involving sums and direct sums of Hilbert space operators. It is shown, among other inequalities, that if X and Y are compact operators, then the singular values of are dominated by those of X ⊕ Y. Applications of these inequalities are also given. 相似文献
13.
Salah Mecheri 《Integral Equations and Operator Theory》2005,53(3):403-409
Let B(H) denote the algebra of all bounded linear operators on a separable infinite dimensional complex Hilbert space H into itself. Let A = (A1,A2,.., An) and B = (B1, B2,.., Bn) be n-tuples in B(H), we define the elementary operator
by
In this paper we initiate the study of some properties of the range of such operators. 相似文献
14.
B. Yousefi 《Archiv der Mathematik》2004,83(6):536-539
Let
be a Hilbert space of functions analytic on a plane domain such that for every in the functional of evaluation at is bounded. Assume further that
contains the constants and admits multiplication by the independent variable z, Mz, as a bounded operator. We give sufficient conditions for Mz to be reflexive.Received: 17 February 2004 相似文献
15.
Letn2. The authors establish theL
2(
n
)-boundedness of singular integrals with variable rough Calderón-Zygmund kernels associated to surfaces satisfying some conditions.The research is supported in part by the NNSF and the SEDF of China. 相似文献
16.
Andrew T. Tomerlin 《Integral Equations and Operator Theory》2000,37(3):350-356
An example is given which clarifies the present situation of the operator norm convergence of Trotter-Kato product formula. It shows that the rate of convergence of the formula with respect to the operator norm obtained in [NZ2] is best possible. It also yields a counter-example of the operator norm convergence of the formula in another case. 相似文献
17.
18.
The Bochner-Martinelli (B.-M.) kernel inherits, forn2, only some of properties of the Cauchy kernel in . For instance it is known that the singular B.-M. operatorM
n
is not an involution forn2. M. Shapiro and N. Vasilevski found a formula forM
2
2
using methods of quaternionic analysis which are essentially complex-twodimensional. The aim of this article is to present a formula forM
n
2
for anyn2. We use now Clifford Analysis but forn=2 our formula coincides, of course, with the above-mentioned one. 相似文献
19.
We consider a generalization of isometric Hilbert space operators to the multivariable setting. We study some of the basic
properties of these tuples of commuting operators and we explore several examples. In particular, we show that the d-shift, which is important in the dilation theory of d-contractions (or row contractions), is a d-isometry. As an application of our techniques we prove a theorem about cyclic vectors in certain spaces of analytic functions
that are properly contained in the Hardy space of the unit ball of
. 相似文献
20.
In previous works we analysed conditions for linearization of Hermitian kernels. The conditions on the kernel turned out to
be of a type considered previously by L. Schwartz in the related matter of characterizing the real linear space generated
by positive definite kernels. The aim of the present note is to find more concrete expressions of the Schwartz type conditions:
in the Hamburger moment problem for Hankel type kernels on the free semigroup, in dilation theory (Stinespring type dilations
and Haagerup decomposability), as well as in multi-variable holomorphy.
Prof. Tiberius Constantinescu died unexpectly on 29th of July 2005. 相似文献