共查询到20条相似文献,搜索用时 0 毫秒
1.
F. A. Sukochev 《Integral Equations and Operator Theory》1996,26(1):102-124
If is a surjective isometry of the separable symmetric operator spaceE(M, ) associated with the approximately finite-dimensional semifinite factorM and if ·
E(M,)
is not proportional to ·
L
2, then there exist a unitary operatorUM and a Jordan automorphismJ ofM such that(x)=UJ(x) for allxME(M, ). We characterize also surjective isometries of vector-valued symmetric spacesF((0, 1), E(M, )).Research supported by the Australian Research Council 相似文献
2.
We show contractibility to a point of the linear group for a wide class of symmetric spaces of measurable operators affiliated with several concrete non-atomic semifinite von Neumann algebras.Research supported by the Australian Research Council 相似文献
3.
We show that ifX is a Banach space of type 2 andG is a compact Abelian group, then any system of eigenvectors {x
}G
(with respect to a strongly continuous representation ofG onX) is an RUC-system. As an application, we exhibit new examples of RUC-bases in certain symmetric spaces of measurable operators.Research supported by the Australian Research Council 相似文献
4.
We investigate some subtle and interesting phenomena in the duality theory of operator spaces and operator algebras, and give several applications of the surprising fact that certain maps are always weak*-continuous on dual spaces. In particular, if X is a subspace of a C*-algebra A, and if a∈A satisfies aX⊂X, then we show that the function x?ax on X is automatically weak* continuous if either (a) X is a dual operator space, or (b) a*X⊂X and X is a dual Banach space. These results hinge on a generalization to Banach modules of Tomiyama's famous theorem on contractive projections onto a C*-subalgebra. Applications include a new characterization of the σ-weakly closed (possibly nonunital and nonselfadjoint) operator algebras, and a generalization of the theory of W*-modules to the framework of modules over such algebras. We also give a Banach module characterization of σ-weakly closed spaces of operators which are invariant under the action of a von Neumann algebra. 相似文献
5.
Fully symmetric operator spaces 总被引:4,自引:0,他引:4
Peter G. Dodds Theresa K. Dodds Ben de Pagter 《Integral Equations and Operator Theory》1992,15(6):942-972
It is shown that certain interpolation theorems for non-commutative symmetric operator spaces can be deduced from their commutative versions. A principal tool is a refinement of the notion of Schmidt decomposition of a measurable operator affiliated with a given semi-finite von Neumann algebra.Research supported by A.R.C. 相似文献
6.
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
7.
This paper deals with the boundary behavior of functions in the de Branges–Rovnyak spaces. First, we give a criterion for
the existence of radial limits for the derivatives of functions in the de Branges–Rovnyak spaces. This criterion generalizes
a result of Ahern–Clark. Then we prove that the continuity of all functions in a de Branges–Rovnyak space on an open arc I of the boundary is enough to ensure the analyticity of these functions on I. We use this property in a question related to Bernstein’s inequality.
Received: May 10, 2007. Revised: August 8, 2007. Accepted: August 8, 2007. 相似文献
8.
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
9.
We answer, by counterexample, several questions concerning algebras of operators on a Hilbert space. The answers add further weight to the thesis that, for many purposes, such algebras ought to be studied in the framework of operator spaces, as opposed to that of Banach spaces and Banach algebras. In particular, the ‘nonselfadjoint analogue’ of a w*-algebra resides naturally in the category of dual operator spaces, as opposed to dual Banach spaces. We also show that an automatic w*-continuity result in the preceding paper of the authors, is sharp. 相似文献
10.
Saida Sultanic 《Integral Equations and Operator Theory》2006,55(4):573-595
The central question of this paper is the one of finding the right analogue of the Commutant Lifting Theorem for the Bergman
space La2. We also analyze the analogous problem for weighted Bergman spaces La,α2, − 1 < α < ∞. 相似文献
11.
We study when a Banach space with absolute norm may have polynomial numerical indices equal to one. In the real case, we show that a Banach space X with absolute norm, which has the Radon-Nikodým property or is Asplund, satisfies n(2)(X)<1 unless it is one-dimensional. In the complex case, we show that the only Banach spaces X with absolute norm and the Radon-Nikodým property which satisfy n(2)(X)=1 are the spaces . Also, the only Asplund complex space X with absolute norm which satisfies n(2)(X)=1 is c0(Λ). 相似文献
12.
We construct an example of a Borel subset E of the unit disk such that area measure restricted to E, which we denote A
E
, has the property that the set of bounded point evaluations for the polynomials with respect to the L
t
(A
E
) norm varies with t. We further show that E can be chosen to be a simply connected region. In the context of smooth measures, like area measure, examples of this type
were unexpected.
相似文献
13.
This paper is a survey of the basics of the theory of two projections. It contains in particular the theorem by Halmos on two orthogonal projections and Roch, Silbermann, Gohberg, and Krupnik’s theorem on two idempotents in Banach algebras. These two theorems, which deliver the desired results usually very quickly and comfortably, are missing or wrongly cited in many recent publications on the topic, The paper is intended as a gentle guide to the field. The basic theorems are precisely stated, some of them are accompanied by full proofs, others not, but precise references are given in each case, and many examples illustrate how to work with the theorems. 相似文献
14.
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
15.
The problem of the multiplication of operators acting in rigged Hilbert spaces is considered. This is done, as usual, by constructing certain intermediate spaces through which the product can be factorized. In the special case where the starting space is the set of C-vectors of a self-adjoint operator A, a general procedure for constructing a special family of interspaces is given. Their definition closely reminds that of the Bessel potential spaces, to which they reduce when the starting space is the Schwartz space
Some applications are considered. 相似文献
16.
Jan van Neerven 《Positivity》2007,11(3):461-467
We give a new proof of a recent characterization by Diaz and Mayoral of compactness in the Lebesgue-Bochner spaces LXp, where X is a Banach space and 1≤ p<∞, and extend the result to vector-valued Banach function spaces EX, where E is a Banach function space with order continuous norm.
The author is supported by the ‘VIDI subsidie’ 639.032.201 in the ‘Vernieuwingsimpuls’ programme of the Netherlands Organization
for Scientific Research (NWO) and by the Research Training Network HPRN-CT-2002-00281. 相似文献
17.
Zhijian Qiu 《Integral Equations and Operator Theory》2006,56(3):415-429
For a compact subset K in the complex plane, let A(K) denote the algebra of all functions continuous on K and analytic on K° and let R(K) denote the uniform closure of the rational functions with poles off K. Let G is a bounded open subset whose complement in the plane has a finite number of components. Suppose that
and every function in H∞(G) is the pointwise limit of a bounded sequence of functions in
. The purpose of this paper is to characterize all subnormal operators similar to Mz, the operator of multiplication by the independent variable z on the Hardy space H2(G). We also characterize all bounded linear operators that are unitarily equivalent to Mz in the case when each of the components of G is simply connected. In particular, our similarity result extends a well-known result of W. Clary on the unit disk to multiply
connected domains. 相似文献
18.
We transfer a large part of the circle of theorems characterizing the generalization of classical H∞ known as ‘weak* Dirichlet algebras’, to Arveson’s very general noncommutative setting of subalgebras of finite von Neumann
algebras. This solves the long-standing open question of the equivalence of principles such as Szeg?’s theorem, the weak*
density of A + A*, and so on, within the noncommutative setting. The techniques should also be useful in future developments in noncommutative
Hp theory. 相似文献
19.
20.
A. Böttcher 《Linear algebra and its applications》2011,435(8):1823-1836
This paper is concerned with algebras generated by two idempotents P and Q satisfying (PQ)m=(QP)m and (PQ)m-1≠(QP)m-1. The main result is the classification of all these algebras, implying that for each m?2 there exist exactly eight nonisomorphic copies. As an application, it is shown that if an element of such an algebra has a nondegenerate leading term, then it is group invertible, and a formula for the explicit computation of the group inverse is given. 相似文献