𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Bounded factorization property for Fréchet spaces

✍ Scribed by Tosun Terzioğlu; Vyacheslav Zahariuta

Publisher
John Wiley and Sons
Year
2003
Tongue
English
Weight
158 KB
Volume
253
Category
Article
ISSN
0025-584X

No coin nor oath required. For personal study only.

✦ Synopsis

Abstract

An operator T ∈ L(E, F) factors over G if T = RS for some S ∈ L(E, G) and R ∈ L(G, F); the set of such operators is denoted by L^G^(E, F). A triple (E, G, F) satisfies bounded factorization property (shortly, (E, G, F) ∈ ℬ︁ℱ) if L^G^(E, F) ⊂ LB(E, F), where LB(E, F) is the set of all bounded linear operators from E to F. The relationship (E, G, F) ∈ ℬ︁ℱ is characterized in the spirit of Vogt's characterisation of the relationship L(E, F) = LB(E, F) [23]. For triples of K�othe spaces the property ℬ︁ℱ is characterized in terms of their K�othe matrices.

As an application we prove that in certain cases the relations L(E, G~1~) = LB(E, G~1~) and L(G~2~, F) = LB(G~2~, F) imply (E, G, F) ∈ ℬ︁ℱ where G is a tensor product of G~1~ and G~2~.

📜 SIMILAR VOLUMES

Local Factorization of Differential Form
Local Factorization of Differential Forms on Fréchet–Schwartz Spaces
✍ Roberto Luiz Soraggi 📂 Article 📅 1997 🏛 Elsevier Science 🌐 English ⚖ 245 KB

The reduction of the Ѩ-problem on a Frechet nuclear space to the study of the Ѩ-operator on a Hilbert space produces a global solution u when the second member w factors globally through this Hilbert space. Easy counterexamples show that this global factorization is not in general possible and hence

A characterization of distinguished Fréc
A characterization of distinguished Fréchet spaces
✍ J. C. Ferrando; J. Ka̧kol; M. López Pellicer 📂 Article 📅 2006 🏛 John Wiley and Sons 🌐 English ⚖ 86 KB

## Abstract Bierstedt and Bonet proved in 1988 that if a metrizable locally convex space __E__ satisfies the Heinrich's density condition, then every bounded set in the strong dual (__E__ ′, __β__ (__E__ ′, __E__)) of __E__ is metrizable; consequently __E__ is distinguished, i.e. (__E__ ′, __β__ (_

On tame pairs of Fréchet spaces
On tame pairs of Fréchet spaces
✍ Krzysztof Piszczek 📂 Article 📅 2009 🏛 John Wiley and Sons 🌐 English ⚖ 206 KB

## Abstract We characterize tame pairs (__X__, __Y__) of Fréchet spaces where either __X__ or __Y__ is a power series space. For power series spaces of finite type, we get the well‐known conditions of (__DN__)‐(Ω) type. On the other hand, for power series spaces of infinite type, surprisingly, tame

Fixed Point Theory for Self Maps between
Fixed Point Theory for Self Maps between Fréchet Spaces
✍ Ravi P. Agarwal; Donal O'Regan 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 118 KB

Using Krasnoselskii's fixed point theorem in a cone, we present a new fixed point theory for multivalued self maps between Frechet spaces. Our analysis relies on a diagonal process and a result on hemicompact maps due to K. K. Tan and X. Z. Ž .