Vector valued invariant means, complementability and almost constrained subspaces

SEMIGROUP ACTIONS , WEAK ALMOST PERIODICITY, AND INVARIANT MEANS

Let S be a topological semigroup acting on a topological space X. We develop the theory of (weakly) almost periodic functions on X, with respect to S, and form the (weakly) almost periodic compactifications of X and S, with respect to each other. We then consider the notion of an action of Son a Banach space, and on its dual, and after defining S-invariant means for such a space, we give a...

Vector-valued Means and Weakly Almost Periodic Functions

Department of Mathematics University of British Columbia Vancouver, B.C., Canada V6T lZ2 (Received June 30, 1992 and in revised form November 7, 1992) ABSTRACT. A formula is set up between vector-vMued mean and scMax-valued that enbles translate many important results about scalar-valued means developed in [1] to vector-valued means. As applications of the theory of vector-vMued means, .how tha...

Almost Self-Bounded Controlled-Invariant Subspaces and Almost Disturbance Decoupling

The objective of this contribution is to characterize the so-called finite fixed poles of the Almost Disturbance Decoupling Problem by state feedback (ADDP) ′ . The most important step towards this result relies on the extension to almost invariant subspaces of the key notion of self-boundedness, as initially introduced by Basile and Marro for perfect controlled-invariants, namely, we introduce...

Central and Almost Constrained Subspaces of Banach Spaces

In this paper we continue the study of central subspaces initiated in [2] and its infinite version called almost constrained subspaces. We are interested in studying situations where these intersection properties of balls lead to the existence of a linear projection of norm one. We show that every finite dimensional subspace is a central subspace only in Hilbert spaces. By considering direct su...

Almost Periodic Invariant Vector Sets in a Metric Vector Space.