Spaces of measurable functions

Diagonal operators on spaces of measurable functions

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Generalized Rings of Measurable and Continuous Functions

This paper is an attempt to generalize, simultaneously, the ring of real-valued continuous functions and the ring of real-valued measurable functions.

On Spaces of Measurable Vector - Valued Functions 399 Proof

Invariant Means on Spaces of Continuous or Measurable Functions ( )

1. Introduction. Invariant means on spaces of functions have been studied by von Neumann [ 7], Banach [ 2], Day [ 4], [5] and others. Day's Amenable semigroups [5] presents a comprehensive summary of the earlier work and many new results. Let 2 be an abstract group or semigroup and ret (2) the Banach space of all bounded real-valued functions on 2 with the supremum norm. A mean on rei(2) is a p...

Reproducing Pairs of Measurable Functions and Partial Inner Product Spaces

We continue the analysis of reproducing pairs of weakly measurable functions, which generalize continuous frames. More precisely, we examine the case where the defining measurable functions take their values in a partial inner product space (PIP spaces). Several examples, both discrete and continuous, are presented.