We show that if X is a L∞-space with the Dieudonnè property and Y is a Banach space not containing l1, then any operator T : X⊗ Y → Z, where Z is a weakly sequentially complete Banach space, is weakly compact. Some other results of the same kind are obtained. Let X be a L∞-space (see [1] for this notion and some useful results on L∞-spaces) and Y be a Banach space not containing l1.We consider ...

We present a 22μW, 2.0GHz FBAR oscillator the lowest power reported to date for a GHz-range oscillator of this type. Low power consumption is achieved through co-design with a high Rp FBAR resonator and a weakly-forward biased bulk connection. An oscillator with a standard bulk connection was fabricated for comparison. The chip was fabricated in a 0.18μm CMOS process. The weakly-forward biased ...

We consider the motion of a particle in a weak mean zero random force field F, which depends on the position, x(t), and the velocity, v(t) = 2(0. The equation of motion is 2(0 = ef(x( t ) , v(t), 0~), where x( ') and v(-) take values in R d, d > 3, and co ranges over some probability space. We show, under suitable mixing and moment conditions on F, that as e--+ 0, v~( t ) v(t/e 2) converges wea...

Let A be a Banach algebra. For f ∈ A*, we inspect the weak sequential properties of well-known map Tf : → (a) = fa, where fa A* is defined by fa(x) (ax) for all x A. We provide equivalent conditions when completely continuous every and maps weakly precompact sets onto L-sets A*. Our results have applications to algebra compact operators K(X) on space X.

We discuss residual finiteness and several related separability conditions for the class of monoid acts, namely weak subact separability, strong complete separability. For each these four conditions, we investigate which monoids have property that all their (finitely generated) acts satisfy condition. In particular, prove that: over a finite are completely separable (and hence other three condi...

Let $WS(X, d)$ be the class of ultrametric spaces which are weakly similar to space $(X, d)$. The main results paper completely describe for equality $$ \rho(x, y) = f(d(\Phi(x), \Phi(y))) holds every $(Y, \rho) \in WS(X, d)$, weak similarity $\Phi \colon Y \to X$, and all $x$, $y Y$ with some (pseudoultrametric) preserving function $f$ depending on $\Phi$.

The co-elementary hierarchy is a nested ordinalindexed sequence of classes of mappings between compacta, with each successor level being defined inductively from the previous one using the topological ultracopower construction. The lowest level is the class of continuous surjections; and the next level up, the co-existential maps, is already a much more restricted class. Co-existential maps are...

In this paper, the Urysohn, completely Hausdorff and completely regular axioms in $L$-topological spaces are generalized to $L$-fuzzy topological spaces. Each $L$-fuzzy topological space can be regarded to be Urysohn, completely Hausdorff and completely regular tosome degree. Some properties of them are investigated. The relations among them and $T_2$ in $L$-fuzzy topological spaces are discussed.

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...