Search results for "Operator space"

Connected components in the space of composition operators onH∞ functions of many variables

2003

LetE be a complex Banach space with open unit ballBe. The structure of the space of composition operators on the Banach algebra H∞, of bounded analytic functions onBe with the uniform topology, is studied. We prove that the composition operators arising from mappings whose range lies strictly insideBe form a path connected component. WhenE is a Hilbert space or aCo(X)- space, the path connected components are shown to be the open balls of radius 2.

Basic Sequences in the Dual of a Fréchet Space

2001

Weakly compact composition operators between algebras of bounded analytic functions

1999

QUASI *-ALGEBRAS OF OPERATORS AND THEIR APPLICATIONS

1995

The main facts of the theory of quasi*-algebras of operators acting in a rigged Hilbert space are reviewed. The particular case where the rigged Hilbert space is generated by a self-adjoint operator in Hilbert space is examined in more details. A series of applications to quantum theories are discussed.

Bounded elements of C*-inductive locally convex spaces

2013

The notion of bounded element of C*-inductive locally convex spaces (or C*-inductive partial *-algebras) is introduced and discussed in two ways: The first one takes into account the inductive structure provided by certain families of C*-algebras; the second one is linked to the natural order of these spaces. A particular attention is devoted to the relevant instance provided by the space of continuous linear maps acting in a rigged Hilbert space.

Absolutely summing operators on C[0,1] as a tree space and the bounded approximation property

2010

Abstract Let X be a Banach space. For describing the space P ( C [ 0 , 1 ] , X ) of absolutely summing operators from C [ 0 , 1 ] to X in terms of the space X itself, we construct a tree space l 1 tree ( X ) on X. It consists of special trees in X which we call two-trunk trees. We prove that P ( C [ 0 , 1 ] , X ) is isometrically isomorphic to l 1 tree ( X ) . As an application, we characterize the bounded approximation property (BAP) and the weak BAP in terms of X ∗ -valued sequence spaces.

On coefficients of vector-valued Bloch functions

2004

Weyl's theorem for perturbations of paranormal operators

2007

A bounded linear operator T ∈ L(X) on a Banach space X is said to satisfy "Weyl's theorem" if the complement in the spectrum of the Weyl spectrum is the set of all isolated points of the spectrum which are eigenvalues of finite multiplicity. In this paper we show that if T is a paranormal operator on a Hilbert space, then T + K satisfies Weyl's theorem for every algebraic operator K which commutes with T.