In this paper we present some generalization (at the same time a new and a short proof in the Banach algebra context) of the Weak Spectral Mapping Theorem (WSMT) for non-quasianalytic representations of oneparameter groups.

Let T be an algebraically paranormal operator acting on Hilbert space. We prove : (i) Weyl’s theorem holds for f(T ) for every f ∈ H(σ(T )); (ii) a-Browder’s theorem holds for f(S) for every S ≺ T and f ∈ H(σ(S)); (iii) the spectral mapping theorem holds for the Weyl spectrum of T and for the essential approximate point spectrum of T . Mathematics Subject Classification (2000). Primary 47A10, 4...

In this note we show the spectral mapping theorem for the evolution semigroup on L p ((; ; X), 1 p < 1, associated with a strongly continuous cocycle on a Banach space over a continuous ow on a locally compact metric space.

in this paper, we introduce the concepts of $2$-isometry, collinearity, $2$%-lipschitz mapping in $2$-fuzzy $2$-normed linear spaces. also, we give anew generalization of the mazur-ulam theorem when $x$ is a $2$-fuzzy $2$%-normed linear space or $im (x)$ is a fuzzy $2$-normed linear space, thatis, the mazur-ulam theorem holds, when the $2$-isometry mapped to a $2$%-fuzzy $2$-normed linear space...

The Mumford conjecture, Madsen-Weiss and homological stability for mapping class groups of surfaces 3 Introduction 3 Lecture 1. The Mumford conjecture and the Madsen-Weiss theorem 5 1. The Mumford conjecture 5 2. Moduli space, mapping class groups and diffeomorphism groups 5 3. The Mumford-Morita-Miller classes 7 4. Homological stability 7 5. The Madsen-Weiss theorem 9 6. Exercices 10 Lecture 2...

generalized geraghty type fuzzy mappings oncomplete metric spaces are introduced and a fixed point theorem thatgeneralizes some recent comparable results for fuzzy mappings incontemporary literature is obtained. example is provided to show thevalidity of obtained results over comparable classical results for fuzzymappings in fixed point theory. as an application, existence of coincidencefuzzy p...

We give necessary and sufficient conditions for a Banach space operator with the single valued extension property (SVEP) to satisfy Weyl’s theorem and a-Weyl’s theorem. We show that if T or T ∗ has SVEP and T is transaloid, then Weyl’s theorem holds for f(T ) for every f ∈ H(σ(T )). When T ∗ has SVEP, T is transaloid and T is a-isoloid, then a-Weyl’s theorem holds for f(T ) for every f ∈ H(σ(T ...

We give necessary and sufficient conditions for a Banach space operator with the single valued extension property (SVEP) to satisfy Weyl’s theorem and a-Weyl’s theorem. We show that if T or T ∗ has SVEP and T is transaloid, then Weyl’s theorem holds for f(T ) for every f ∈ H(σ(T )). When T ∗ has SVEP, T is transaloid and T is a-isoloid, then a-Weyl’s theorem holds for f(T ) for every f ∈ H(σ(T ...

In this note, we aim to present some properties of the space of all weakly fuzzy bounded linear operators, with the Bag and Samanta’s operator norm on Felbin’s-type fuzzy normed spaces. In particular, the completeness of this space is studied. By some counterexamples, it is shown that the inverse mapping theorem and the Banach-Steinhaus’s theorem, are not valid for this fuzzy setting. Also...