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Strictly Cyclic Functionals, Reflexivity, and Hereditary Reflexivity of Operator Algebras [PDF]
Abstract and Applied Analysis, 2012 This paper is concerned with strictly cyclic functionals of operator algebras on Banach spaces. It is shown that if X is a reflexive Banach space and A is a norm-closed semisimple abelian subalgebra of B(X) with a strictly cyclic functional f∈X∗, then A ...
Quanyuan Chen, Xiaochun Fang
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Normalizers of Operator Algebras and Reflexivity [PDF]
Proceedings of the London Mathematical Society, 2002 The set of normalizers between von Neumann (or, more generally, reflexive) algebras A and B, (that is, the set of all operators x such that xAx* is a subset of B and x*Bx is a subset of A) possesses `local linear structure': it is a union of reflexive ...
Katavolos, A., Todorov, I. G.
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The carrier space of a reflexive operator algebra [PDF]
Pacific Journal of Mathematics, 1979 Many properties of nest algebras are actually valid for reflexive operator algebras with a commutative subspace lattice. In this paper we collect a number of such results related to the carrier space of the algebra. Included among these results are a generalization of Ringrose's criterion, a description of the partial correspondence between lattice ...
Hopenwasser, Alan, Larson, David
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The radical of a reflexive operator algebra [PDF]
Pacific Journal of Mathematics, 1976 The radical of a reflexive operator algebra % whose lattice of invariant subspaces 2 is commutative is related to the space of lattice homomorphisms of 2 onto {0,1}. To each such homomorphism φ is associated a closed, two-sided ideal Wψ contained in H.
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Higher Weak Derivatives and Reflexive Algebras of Operators
, 2015 Let D be a self-adjoint operator on a Hilbert space H and x a bounded operator on H. We say that x is n-times weakly D-differentiable, if for any pair of vectors a, b from H the function is n-times differentiable.
Christensen, Erik
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2-hyperreflexivity and hyporeflexivity of power partial isometries [PDF]
Opuscula Mathematica, 2016 Power partial isometries are not always hyperreflexive neither reflexive. In the present paper it will be shown that power partial isometries are always hyporeflexive and \(2\)-hyperreflexive.
Kamila Piwowarczyk, Marek Ptak
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Reflexive operator algebras on Banach spaces [PDF]
Pacific Journal of Mathematics, 2014 In this paper we study the reflexivity of a unital strongly closed algebra of operators with complemented invariant subspace lattice on a Banach space. We prove that if such an algebra contains a complete Boolean algebra of projections of finite uniform multiplicity and with the direct sum property, then it is reflexive, i.e. it contains every operator
Merlevède, Florence +2 more
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Operators acting on certain Banach spaces of analytic functions
International Journal of Mathematics and Mathematical Sciences, 1995 Let 𝒳 be reflexive Banach space of functions analytic plane domain Ω such that for every λ in Ω the functional of evaluation at λ is bounded. Assume further that 𝒳 contains the constants and Mz multiplication by the independent variable z, is bounded ...
K. Seddighi, K. Hedayatiyan, B. Yousefi
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A bicommutant theorem for dual Banach algebras [PDF]
, 2010 A dual Banach algebra is a Banach algebra which is a dual space, with the multiplication being separately weak$^*$-continuous. We show that given a unital dual Banach algebra $\mc A$, we can find a reflexive Banach space $E$, and an isometric, weak ...
Daws, Matthew
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, 2014 An LDB division algebra is a triple $(A,\star,\bullet)$ in which $\star$ and $\bullet$ are regular bilinear laws on the finite-dimensional non-zero vector space $A$ such that $x \star (x \bullet y)$ is a scalar multiple of $y$ for all vectors $x$ and $y$
Pazzis, Clément de Seguins
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