Search results for "Functional analysis"

A non-linear version of Hunt-Lion's theorem from the point of view of T-accretivity

1992

In the classical topological context, Dellacherie [10] has given a non-linear version of Hunt's theorem characterizing the proper kernels verifying the complete maximum principle as those closing a submarkovian resolvent. In this paper we study the relation between this non-linear version of Hunt's theorem and T-accretivity.

On the Russo-Dye Theorem for positive linear maps

2019

Abstract We revisit a classical result, the Russo-Dye Theorem, stating that every positive linear map attains its norm at the identity.

Lineability of non-differentiable Pettis primitives

2014

Let \(X\) be an infinite-dimensional Banach space. In 1995, settling a long outstanding problem of Pettis, Dilworth and Girardi constructed an \(X\)-valued Pettis integrable function on \([0,1]\) whose primitive is nowhere weakly differentiable. Using their technique and some new ideas we show that \(\mathbf{ND}\), the set of strongly measurable Pettis integrable functions with nowhere weakly differentiable primitives, is lineable, i.e., there is an infinite dimensional vector space whose nonzero vectors belong to \(\mathbf{ND}\).

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.

On the boundary spectrum of dominatedC o-Semigroups

1989

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.

Gleason Parts and Weakly Compact Homomorphismsbetween Uniform Banach Algebras

1999

If points in nontrivial Gleason parts of a uniform Banach algebra have unique representing measures, then the weak and the norm topology coincide on the spectrum. We derive from this several consequences about weakly compact homomorphisms and discuss the case of other uniform Banach algebras arising in complex infinite dimensional analysis.

A theorem of insertion and extension of functions for normal spaces

1993

The Fine Spectre of Some Cesàro Generalized Operators Defined onℓp(p> 1)

2004

Abstract The aim of the paper is the study of the fine spectre for a class of Cesaro generalized operators, Rhaly operators, when those operators are defined on the spaces lp, p > 1.

The spectra of some algebras of analytic mappings

1999

Abstract Let E be a Banach space with the approximation property and let F be a Banach algebra with identity. We study the spectrum of the algebra H b(E, F) of all holomorphic mappings f : E → F that are bounded on the bounded subsets of E.