Search results for " Operator"
showing 10 items of 931 documents
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 ).
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 .
Compact and Weakly Compact Homomorphisms on Fréchet Algebras of Holomorphic Functions
2002
We study homomorphisms between Frechet algebras of holomorphic functions of bounded type. In this setting we prove that any pointwise bounded homomorphism into the space of entire functions of bounded type is rank one. We characterize up to the approximation property of the underlying Banach space, the weakly compact composition operators on Hb(V), V absolutely convex open set.
On certain linear operators in spaces of ultradifferentiable functions
1996
Let ω be a weight in the sense of Braun, Meise, Taylor, which defines a non-quasianalytic class. Let H be a compact subset of ℝn. It is proved that for every function ƒ on ℝn which belongs to the non-quasianalytic (ω)-class, there is an element g of the same class which is analytic on ℝn\H and such that Dαƒ(x) = Dαg(x) for every x ∈ H and α ∈ ℕ0n. A similar result is proved for functions of the Roumieu type. Continuous linear extension operators of Whitney jets with additional properties are also obtained.
Composition operators on uniform algebras, essential norms, and hyperbolically bounded sets
2006
Let A be a uniform algebra, and let o be a self-map of the spectrum M A of A that induces a composition operator C o on A. The object of this paper is to relate the notion of "hyperbolic boundedness" introduced by the authors in 2004 to the essential spectrum of C o . It is shown that the essential spectral radius of C o , is strictly less than 1 if and only if the image of M A under some iterate o n of o is hyperbolically bounded. The set of composition operators is partitioned into "hyperbolic vicinities" that are clopen with respect to the essential operator norm. This partition is related to the analogous partition with respect to the uniform operator norm.