scholarly journals On isomorphisms and hyper-reflexivity of closed subspace lattices

1991 ◽  
Vol 14 (3) ◽  
pp. 447-450
Author(s):  
Han Deguang
Keyword(s):  
Hilbert Spaces ◽  
Closed Subspace ◽  
Short Paper ◽  
Subspace Lattice ◽  
Reflexive Subspace ◽  
Subspace Lattices

There are some papers, such as [1], [2] and [3], in which some properties on isomorphism of closed subspace lattices of Hilbert spaces were studied. In this short paper we will point out that the hyper-reflexivity of closed subspace lattice is invariant under isomorphism ofξ(H1)onξ(H2). We also proved that ifTis inL(H)such that0∈¯π(T)andℱis a hyper-reflexive subspace lattice, thenϕT(ℱ)∪{H}is hyper-reflexive whereϕTis a homomorphism induced byT.

The Tensor Product Formula for Reflexive Subspace Lattices

1995 ◽  
Vol 38 (3) ◽  
pp. 308-316 ◽  
Author(s):  
K. J. Harrison
Keyword(s):  
Tensor Product ◽  
Operator Algebra ◽  
Product Formula ◽  
Completely Distributive ◽  
Reflexive Subspace ◽  
Complemented Lattice ◽  
Csl Algebra ◽  
Subspace Lattices

AbstractWe give a characterisation of where and are subspace lattices with commutative and either completely distributive or complemented. We use it to show that Lat is a CSL algebra with a completely distributive or complemented lattice and is any operator algebra.

scholarly journals Derivations, local derivations and atomic boolean subspace lattices

2002 ◽  
Vol 66 (3) ◽  
pp. 477-486 ◽  
Author(s):  
Pengtong Li ◽  
Jipu Ma
Keyword(s):  
Banach Space ◽  
Linear Operator ◽  
Closed Linear Operator ◽  
Subspace Lattice ◽  
Local Derivation ◽  
Densely Defined ◽  
Subspace Lattices

Let ℒ be an atomic Boolean subspace lattice on a Banach space X. In this paper, we prove that if ℳ is an ideal of Alg ℒ then every derivation δ from Alg ℒ into ℳ is necessarily quasi-spatial, that is, there exists a densely defined closed linear operator T: 𝒟(T) ⊆ X → X with its domain 𝒟(T) invariant under every element of Alg ℒ, such that δ(A) x = (TA – AT) x for every A ∈ Alg ℒ and every x ∈ 𝒟(T). Also, if ℳ ⊆ ℬ(X) is an Alg ℒ-module then it is shown that every local derivation from Alg ℒ into ℳ is necessary a derivation. In particular, every local derivation from Alg ℒ into ℬ(X) is a derivation and every local derivation from Alg ℒ into itself is a quasi-spatial derivation.

scholarly journals A SPECTRAL CHARACTERIZATION OF OPERATORS

2016 ◽  
Vol 102 (3) ◽  
pp. 369-391 ◽  
Author(s):  
SATISH K. PANDEY ◽  
VERN I. PAULSEN
Keyword(s):  
Banach Space ◽  
Hilbert Spaces ◽  
Real Banach Space ◽  
Closed Subspace ◽  
Characterization Theorem ◽  
Positive Operators ◽  
Spectral Characterization ◽  
Proper Cone ◽  
Arbitrary Dimensions

We establish a spectral characterization theorem for the operators on complex Hilbert spaces of arbitrary dimensions that attain their norm on every closed subspace. The class of these operators is not closed under addition. Nevertheless, we prove that the intersection of these operators with the positive operators forms a proper cone in the real Banach space of hermitian operators.

Non-Operator Reflexive Subspace Lattices

2008 ◽  
Vol 62 (4) ◽  
pp. 595-599 ◽  
Author(s):  
Kamila Kliś-Garlicka ◽  
Vladimir Müller
Keyword(s):  
Reflexive Subspace ◽  
Subspace Lattices

Structure in Reflexive Subspace Lattices

1982 ◽  
Vol s2-26 (1) ◽  
pp. 117-131 ◽  
Author(s):  
Frank Gilfeather ◽  
David R. Larson
Keyword(s):  
Reflexive Subspace ◽  
Subspace Lattices

An Existence Result for Stepanoff Almost-Periodic Differential Equations

1971 ◽  
Vol 14 (4) ◽  
pp. 551-554 ◽  
Author(s):  
S. Zaidman
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Hilbert Spaces ◽  
Existence Result ◽  
Order Differential Equation ◽  
Short Paper ◽  
Almost Periodic ◽  
First Order ◽  
Right Hand

In this short paper we present an existence (an unicity) result for a first order differential equation in Hilbert spaces with right-hand side almost-periodic in the sense of Stepanoff.

scholarly journals Best approximation in Orlicz spaces

1991 ◽  
Vol 14 (2) ◽  
pp. 245-252 ◽  
Author(s):  
H. Al-Minawi ◽  
S. Ayesh
Keyword(s):  
Banach Space ◽  
Continuous Function ◽  
Best Approximation ◽  
Measure Space ◽  
Real Banach Space ◽  
Closed Subspace ◽  
Orlicz Spaces ◽  
Finite Measure ◽  
Reflexive Subspace ◽  
Finite Measure Space

LetXbe a real Banach space and(Ω,μ)be a finite measure space andϕbe a strictly icreasing convex continuous function on[0,∞)withϕ(0)=0. The spaceLϕ(μ,X)is the set of all measurable functionsfwith values inXsuch that∫Ωϕ(‖c−1f(t)‖)dμ(t)<∞for somec>0. One of the main results of this paper is: “For a closed subspaceYofX,Lϕ(μ,Y)is proximinal inLϕ(μ,X)if and only ifL1(μ,Y)is proximinal inL1(μ,X)′​′. As a result ifYis reflexive subspace ofX, thenLϕ(ϕ,Y)is proximinal inLϕ(μ,X). Other results on proximinality of subspaces ofLϕ(μ,X)are proved.

Generalized frames for operators in Hilbert spaces

2014 ◽  
Vol 17 (02) ◽  
pp. 1450013 ◽  
Author(s):  
Mohammad Sadegh Asgari ◽  
Hamidreza Rahimi
Keyword(s):  
Hilbert Space ◽  
Hilbert Spaces ◽  
Separable Hilbert Space ◽  
Closed Subspace ◽  
Bounded Operator ◽  
Riesz Bases ◽  
Small Perturbations ◽  
Riesz Decomposition ◽  
Analysis And Synthesis ◽  
General Range

In this paper we present a family of analysis and synthesis systems of operators with frame-like properties for the range of a bounded operator on a separable Hilbert space. This family of operators is called a Θ–g-frame, where Θ is a bounded operator on a Hilbert space. Θ–g-frames are a generalization of g-frames, which allows to reconstruct elements from the range of Θ. In general, range of Θ is not a closed subspace. We also construct new Θ–g-frames by considering Θ–g-frames for its components. We further study Riesz decompositions for Hilbert spaces, which are a generalization of the notion of Riesz bases. We define the coefficient operators of a Riesz decomposition and we will show that these coefficient operators are continuous projections. We obtain some results about stability of Riesz decompositions under small perturbations.

scholarly journals Generalized Derivations and Bilocal Jordan Derivations of Nest Algebras

2011 ◽  
Vol 2011 ◽  
pp. 1-6
Author(s):  
Dangui Yan ◽  
Chengchang Zhang
Keyword(s):  
Hilbert Space ◽  
Closed Subspace ◽  
Complex Hilbert Space ◽  
Generalized Derivations ◽  
Nest Algebra ◽  
Bounded Operators ◽  
Subspace Lattice ◽  
Nest Algebras

LetHbe a complex Hilbert space andB(H)the collection of all linear bounded operators,Ais the closed subspace lattice including 0 anH, thenAis a nest, accordingly algA={T∈B(H):TN⊆N,  ∀N∈A}is a nest algebra. It will be shown that of nest algebra, generalized derivations are generalized inner derivations, and bilocal Jordan derivations are inner derivations.

scholarly journals Tensor products of reflexive subspace lattices.

1984 ◽  
Vol 31 (3) ◽  
pp. 359-370 ◽  
Author(s):  
Alan Hopenwasser
Keyword(s):  
Tensor Products ◽  
Reflexive Subspace ◽  
Subspace Lattices
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