Vector-valued means and weakly almost periodic functions (Q1326605)

The article transposes basic results on invariant means to the larger situation concerning vector-valued means. If \(A\) is a linear space of bounded mappings from the semigroup \(S\) into the Banach space \(X\), a linear mapping \(\mu : A \to X\) is called mean if \(\mu(f) = \overline{co} f(S)\) whenever \(f \in A\). For the subject a relevant earlier reference is \textit{T. Husain} and \textit{J. C. S. Wong} [Ann. Sc. Norm. Super. Pisa, Sci. Fis. Mat., III. Ser. 27, 717-727, 729-742 (1974; Zbl 0317.43005)]. Additionally weakly almost periodic vector-valued functions are investigated.