ON A LOCALISED SINGLE-VALUED EXTENSION PROPERTY By PIETRO AIENA
نویسنده
چکیده
In this article, we investigate, a certain localised version of the single-valued extension property for a bounded linear operator on a Banach space. We show that this condition behaves canonically under the Riesz functional calculus, and derive a number of characterisations in terms of kernel-type and range-type spaces for the operator and its adjoint. The theory is exemplified in the case of isometries, analytic Toeplitz operators, invertible composition operators on Hardy spaces, and weighted shifts.
منابع مشابه
Single Valued Extension Property and Generalized Weyl’s Theorem
Let T be an operator acting on a Banach space X, let σ(T ) and σBW (T ) be respectively the spectrum and the B-Weyl spectrum of T . We say that T satisfies the generalized Weyl’s theorem if σBW (T ) = σ(T ) \E(T ), where E(T ) is the set of all isolated eigenvalues of T . The first goal of this paper is to show that if T is an operator of topological uniform descent and 0 is an accumulation poi...
متن کاملSome Connections between an Operator and Its Aluthge Transform
Associated with T = U|T | (polar decomposition) in L(H) is a related operator T̃ = |T | 1 2U|T | 1 2 , called the Aluthge transform of T . In this paper we study some connections betweenT and T̃ , including the following relations; the single valued extension property, an analogue of the single valued extension property onWm(D,H), Dunford’s property (C) and the property (β). 2000 Mathematics Subj...
متن کاملCohyponormal Operators with the Single Valued Extension Property
It is proved that in order to find a nontrivial hyperinvariant subspace for a cohyponormal operator it suffices to make the further assumption that the operator have the single-valued extension property.
متن کاملCharacterization of weak fixed point property for new class of set-valued nonexpansive mappings
In this paper, we introduce a new class of set-valued mappings which is called MD-type mappings. This class of mappings is a set-valued case of a class of the D-type mappings. The class of D-type mappings is a generalization of nonexpansive mappings that recently introduced by Kaewkhao and Sokhuma. The class of MD-type mappings includes upper semi-continuous Suzuki type mappings, upper semi-con...
متن کامل(JCLR) property and fixed point in non-Archimedean fuzzy metric spaces
The aim of the present paper is to introduce the concept of joint common limit range property ((JCLR) property) for single-valued and set-valued maps in non-Archimedean fuzzy metric spaces. We also list some examples to show the difference between (CLR) property and (JCLR) property. Further, we establish common fixed point theorems using implicit relation with integral contractive condition. Se...
متن کامل