Search results for "Operator"
showing 10 items of 1427 documents
Pietsch's factorization theorem for dominated polynomials
2007
Abstract We prove that, like in the linear case, there is a canonical prototype of a p -dominated homogeneous polynomial through which every p -dominated polynomial between Banach spaces factors.
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.
Property (R) under perturbations
2012
Property (R) holds for a bounded linear operator $${T \in L(X)}$$ , defined on a complex infinite dimensional Banach space X, if the isolated points of the spectrum of T which are eigenvalues of finite multiplicity are exactly those points λ of the approximate point spectrum for which λI − T is upper semi-Browder. In this paper we consider the permanence of this property under quasi nilpotent, Riesz, or algebraic perturbations commuting with T.
Property (R) for Bounded Linear Operators
2011
We introduce the spectral property (R), for bounded linear operators defined on a Banach space, which is related to Weyl type theorems. This property is also studied in the framework of polaroid, or left polaroid, operators.
On linear extension operators from growths of compactifications of products
1996
Abstract We obtain some results on product spaces. Among them we prove that for noncompact spaces X 1 and X 2 , the norm of every linear extension operator from C ( β ( X 1 × X 2 ) β ( X 1 × X 2 )) into C ( β ( X 1 × X 2 )) is greater or equal than 2, and also that β ( X 1 × X 2 ) β ( X 1 × X 2 ) is not a neighborhood retract of β ( X 1 × X 2 ).
Lp-Spaces as Quasi *-Algebras
1996
Abstract The Banach space L p ( X , μ), for X a compact Hausdorff measure space, is considered as a special kind of quasi *-algebra (called CQ*-algebra) over the C*-algebra C ( X ) of continuous functions on X . It is shown that, for p ≥2, ( L p ( X , μ), C ( X )) is *-semisimple (in a generalized sense). Some consequences of this fact are derived.
Non-self-adjoint resolutions of the identity and associated operators
2013
Closed operators in Hilbert space defined by a non-self-adjoint resolution of the identity $$\{X(\lambda )\}_{\lambda \in {\mathbb R}}$$ , whose adjoints constitute also a resolution of the identity, are studied. In particular, it is shown that a closed operator $$B$$ has a spectral representation analogous to the familiar one for self-adjoint operators if and only if $$B=\textit{TAT}^{-1}$$ where $$A$$ is self-adjoint and $$T$$ is a bounded inverse.
The p-Laplacian with respect to measures
2013
We introduce a definition for the $p$-Laplace operator on positive and finite Borel measures that satisfy an Adams-type embedding condition.
Lipschitz operator ideals and the approximation property
2016
[EN] We establish the basics of the theory of Lipschitz operator ideals with the aim of recovering several classes of Lipschitz maps related to absolute summability that have been introduced in the literature in the last years. As an application we extend the notion and main results on the approximation property for Banach spaces to the case of metric spaces. (C) 2015 Elsevier Inc. All rights reserved.
Property (w) and perturbations
2007
A bounded linear operator T ∈ L(X) defined on a Banach space X satisfies property (w), a variant of Weyl’s theorem, if the complement in the approximate point spectrum σa(T ) of the Weyl essential approximate spectrum σwa(T ) coincides with the set of all isolated points of the spectrum which are eigenvalues of finite multiplicity. In this note, we study the stability of property (w), for a bounded operator T acting on a Banach space, under perturbations by finite rank operators, by nilpotent operator and quasi-nilpotent operators commuting with T .