Convex programming on spaces of measurable functions

Diagonal operators on spaces of measurable functions

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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...

Uniformly Convex Functions on Banach Spaces

We study the connection between uniformly convex functions f : X → R bounded above by ‖ · ‖p, and the existence of norms on X with moduli of convexity of power type. In particular, we show that there exists a uniformly convex function f : X → R bounded above by ‖ · ‖2 if and only if X admits an equivalent norm with modulus of convexity of power type 2.

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.