Displaying similar documents to “Some results on composition operators on ℓ 2 .”

Linear maps preserving quasi-commutativity

Heydar Radjavi, Peter Šemrl (2008)

Studia Mathematica

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Let X and Y be Banach spaces and ℬ(X) and ℬ(Y) the algebras of all bounded linear operators on X and Y, respectively. We say that A,B ∈ ℬ(X) quasi-commute if there exists a nonzero scalar ω such that AB = ωBA. We characterize bijective linear maps ϕ : ℬ(X) → ℬ(Y) preserving quasi-commutativity. In fact, such a characterization can be proved for much more general algebras. In the finite-dimensional case the same result can be obtained without the bijectivity assumption.

On Quasi-Normality of Two-Sided Multiplication

Amouch, M. (2009)

Serdica Mathematical Journal

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2000 Mathematics Subject Classification: 47B47, 47B10, 47A30. In this note, we characterize quasi-normality of two-sided multiplication, restricted to a norm ideal and we extend this result, to an important class which contains all quasi-normal operators. Also we give some applications of this result.

A quasi-affine transform of an unbounded operator

Schôichi Ôta (1995)

Studia Mathematica

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Some results on quasi-affinity for bounded operators are extended to unbounded ones and normal extensions of an unbounded operator are discussed in connection with quasi-affinity.

A remark on the range of elementary operators

Said Bouali, Youssef Bouhafsi (2010)

Czechoslovak Mathematical Journal

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Let L ( H ) denote the algebra of all bounded linear operators on a separable infinite dimensional complex Hilbert space H into itself. Given A ∈ L ( H ) , we define the elementary operator Δ A : L ( H ) ⟶ L ( H ) by Δ A ( X ) = A X A - X . In this paper we study the class of operators A ∈ L ( H ) which have the following property: A T A = T implies A T * A = T * for all trace class operators T ∈ C 1 ( H ) . Such operators are termed generalized quasi-adjoints. The main result is the equivalence between this character and the fact that the ultraweak closure of the range of Δ A is closed...

Quasi-linear maps

D. J. Grubb (2008)

Fundamenta Mathematicae

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A quasi-linear map from a continuous function space C(X) is one which is linear on each singly generated subalgebra. We show that the collection of quasi-linear functionals has a Banach space pre-dual with a natural order. We then investigate quasi-linear maps between two continuous function spaces, classifying them in terms of generalized image transformations.

Versatile asymmetrical tight extensions

Olivier Olela Otafudu, Zechariah Mushaandja (2017)

Topological Algebra and its Applications

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We show that the image of a q-hyperconvex quasi-metric space under a retraction is q-hyperconvex. Furthermore, we establish that quasi-tightness and quasi-essentiality of an extension of a T0-quasi-metric space are equivalent.