Results 121 to 130 of about 15,515 (151)

Operators of Rank One in Reflexive Algebras

Canadian Journal of Mathematics, 1976
If H is a (complex) Hilbert space and is a collection of (closed linear) subspaces of H it is easily shown that the set of all (bounded linear) operators acting on H which leave every member of invariant is a weakly closed operator algebra containing the identity operator. This algebra is denoted by Alg .
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Derivations and isomorphisms of certain reflexive operator algebras

Acta Mathematica Sinica, 1998
Summary: We prove that every derivation of completely distributive subspace lattice (CDS) algebras on Banach space is automatically continuous. This is new even in the Hilbert space case. As an application of this result, we obtain that every additive derivation of nest algebras on Banach spaces is inner.
Hou, Chengjun, Han, Deguang
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On the Reflexivity of Operator Algebras with Isometric Functional Calculus

Journal of the London Mathematical Society, 2000
The authors generalize the theorem by Brown and Chevreau that every absolutely continuous contraction in \({\mathcal L}(H)\) is reflexive in case it has an isometric \(H^\infty\)-functional calculus. They show that every subalgebra of \({\mathcal L}(H)\) which is isometrically weak\(^*\)-homeomorphic with \(H^\infty(\Omega)\) is reflexive, if \(\Omega\)
PATA, VITTORINO, K. X. Zheng, A. Zucchi
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On A-Submodules for Reflexive Operator Algebras

Proceedings of the American Mathematical Society, 1988
In [2] the authors described all weakly closed _W-submodules of L(H) for a nest algebra v in terms of order homomorphisms of Lat-'. In this paper we prove that for any reflexive algebra v which is a-weakly generated by rank-one operators in X, every a-weakly closed s/-submodule can be characterized by an order homomorphism of Lat-W.
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Cyclic Banach spaces and reflexive operator algebras

Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 1978
SynopsisLet X be a Banach space and let ℬ be a σ-complete Boolean algebra of projections on X with a cyclic vector. It is shown that there exists a normed Köthe space Lρ, the norm of which has the Fatou property, such that X is linearly homeomorphic to the subspace of Lρ consisting of those functions of absolutely continuous norm and such that, under ...
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σ-Weakly Closed Modules of Certain Reflexive Operator Algebras

Proceedings of the American Mathematical Society, 1995
Summary: Let \(\mathcal A\) be a completely distributive CSL algebra and let \(M\) be any \(\sigma\)-weakly closed \(\mathcal A\)-module. We give characterizations of commutant \(C({\mathcal A}, M)\) of \(\mathcal A\) modulo \(M\) and \(\text{AlgLat }M\).
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On Algebras of Relations with Operations of Left and Right Reflexive Product

Lobachevskii Journal of Mathematics, 2020
This paper investigates the classes of ordered and unordered algebras, \((A, \ast, \subseteq)\) or \((A, \ast)\), where \(A\) is a set of binary relations on some set, \(\subseteq\) is set-theoretical inclusion, and the binary operation \(\ast\) is defined by \[ \rho\ast \sigma = \{(u,v)\;:\;(\exists w)((u,u)\in\rho\;\wedge (w,w)\in \sigma)\}.
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Finite Rank Operators in Reflexive Operator Algebras

Journal of the London Mathematical Society, 1983
Hopenwasser, Alan, Moore, Robert
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On Strictly Cyclic Algebras, -Algebras and Reflexive Operators

Transactions of the American Mathematical Society, 1973
Herrero, Domingo A., Lambert, Alan
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Interpolation problems for Hilbert-Schmidt operators in reflexive algebras

2019
Given two collections of \(n\)-vectors \(\{x_ 1,x_ 2,\dots, x_ n\}\) and \(\{y_ 1, y_ 2,\dots, y_ n\}\) in a Hilbert space \(\mathcal H\) we are interested in the existence of an operator \(T\) such that \(Tx_ i= y_ i\), \(i= 1,\dots, n\). Such a problem is called the \(n\)-vector interpolation problem.
Katsoulis, Eg, Anousis, M, Moore, Rl, Trent, Tt   +3 more
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