A combinatorial principle CECA is formulated and its equivalence with GCH + certain weakenings of 2λ for singular λ is proved. CECA is used to show that certain “almost point-< τ” families can be refined to point-< τ families by removing a small set from each member of the family. This theorem in turn is used to show the consistency of “every first countable T1-space with a weakly uniform base ...

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...

It is shown that the collection of weakly almost periodic functionals on the convolution algebra of a commutative Hopf von Neumann algebra is a C∗-algebra. This implies that the weakly almost periodic functionals on M(G), the measure algebra of a locally compact group G, is a C∗-subalgebra of M(G)∗ = C0(G) ∗∗. The proof builds upon a factorisation result, due to Young and Kaiser, for weakly com...

A theorem of Davis, Figiel, Johnson and Pe lczyński tells us that weakly-compact operators between Banach spaces factor through reflexive Banach spaces. The machinery underlying this result is that of the real interpolation method, which has been adapted to the category of operator spaces by Xu, showing the this factorisation result also holds for completely bounded weakly-compact maps. In this...

We characterize the weak almost periodicity of a vector-valued, bounded, continuous function. We show that if the range of the function is relatively weakly compact, then the relative weak compactness of its right orbit is equivalent to that of its left orbit. At the same time, we give the function some other equivalent properties. 1. Introduction. Let S be a semitopological semigroup, let ᐄ be...