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Some problems concerning different types of vector valued almost periodic functions

Bolis Basit — 1995

CONTENTS   Introduction.............................................................51. Notation, preliminaries, main definitions and solution of problem (D)...................6   1.1. Notation............................................................6   1.2. Preliminaries.......................................................7   1.3. Main definitions....................................................8   1.4. Problem (D).........................................................82. Examples of...

Convergence of Fourier series of almost periodic functions with values in Banach spaces

Bolis Basit — 1976

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti

La presente Nota concerne la convergenza delle serie di Fourier di funzioni q.p. a valori in uno spazio di Banach. Si assegna una condizione necessaria e sufficiente perché una serie debolmente incondizionatamente convergente lo sia fortemente. Si dimostra inoltre che in certi spazi di Banach ( C ⁢ ( Q ) , L p ⁢ ( a , b ) , l p ) se i coefficienti di Fourier sono positivi, allora la serie di Fourier è fortemente incondizionatamente convergente.

Strong continuity of semigroup homomorphisms

Bolis Basit;  A. Pryde — 1999

Studia Mathematica

Let J be an abelian topological semigroup and C a subset of a Banach space X. Let L(X) be the space of bounded linear operators on X and Lip(C) the space of Lipschitz functions ⨍: C → C. We exhibit a large class of semigroups J for which every weakly continuous semigroup homomorphism T: J → L(X) is necessarily strongly continuous. Similar results are obtained for weakly continuous homomorphisms T: J → Lip(C) and for strongly measurable homomorphisms T: J → L(X).

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