Let $T$ be a bounded operator on the Banach space $X$ and $ph$ be an analytic self-map of the unit disk $Bbb{D}$‎. ‎We investigate some operator theoretic properties of‎ ‎bilateral composition operator $C_{ph‎, ‎T}‎: ‎f ri T circ f circ ph$ on the vector-valued Hardy space $H^p(X)$ for $1 leq p leq‎ ‎+infty$.‎ ‎Compactness and weak compactness of $C_{ph‎, ‎T}$ on $H^p(X)$‎ ‎are characterized an...

In this paper we present a brief review of some important results on weak compactness in the space of vector valued measures. We also review some recent results of the author on weak compactness of any set of operator valued measures. These results are then applied to optimal structural feedback control for deterministic systems on infinite dimensional spaces.

We will use the concept of strong generating and a simple renorming theorem to give new proofs to slight generalizations of some results of Argyros and Rosenthal on weakly compact sets in L1(μ) spaces for finite measures μ. The purpose of this note is to show that a simple transfer renorming theorem explains why L1(μ)-spaces, for finite measures μ, share some properties with superreflexive spac...

One of the most important goals of set theorists over the last few years has been to re-prove old results which previously had used very strong assumptions from hypotheses which, at least prima facie, are weaker. Examples of these abound, including, but certainly not limited to, the work of Woodin and Cummings (see [3]) on the Singular Cardinals Problem, in which results previously obtained by ...

In this paper we obtain some versions of weak compactness James’ theorem, replacing bounded linear functionals by polynomials and symmetric multilinear forms. Mathematics Subject Classification (1991): 46B10, 46B50, 46G25

Let (Q.,l,ß) be a probability space, X a Banach space, and L (fi, X) the Banach space of Bochner integrable functions f: Í2 —> X . Let W = {/ € Ll(p, X) : for a.e. w in Í2, ||/(w)|| < 1} . In this paper we characterize the rwc (relatively weakly compact) subsets of L (ß, X). The main results are as follows: Theorem A. A subset H of W is rwc iff given any sequence (/„) in H there exists a sequen...

We present a characterization of weakly compact cardinals in terms of generalized stationarity. We apply this characterization to construct a model with no partial square sequences. One of the striking features of weak compactness in the large cardinal hierarchy is the wide variety of characterizations of the concept. These characterizations meet many disparate areas of set theory, including me...

We explore the connection between the concepts “excess” and “duality gap” from epigraphical analysis and optimization, and the functional analytic concepts of weak* and weak compactness. We also discuss briefly the connection with R. C. James’s “sup theorem”.

In this paper we obtain some properties of the weak smooth α-closure and weak smooth α-interior of a fuzzy set in smooth topological spaces and introduce the concepts of several types of weak∗ smooth compactness in smooth topological spaces and investigate some of their properties.