Several recent papers investigated unbounded convergences in Banach lattices. The focus of this paper is to apply the results convergence classical lattice theory from a new perspective. Combining all convergences, including order (norm, absolute weak, weak*) convergence, we characterize L-weakly compact sets, operators and M-weakly on For applications, introduce so-called statistical-unbounded...

We consider the space of weakly almost periodic functions on a transformation semigroup (S, X , ?) and show that if X is a locally compact noncompact uniform space, and ? is a separately continuous, separately proper, and equicontinuous action of S on X, then every continuous function on X, vanishing at infinity is weakly almost periodic. We also use a number of diverse examples to show ...

Although various operators in the space of functions bounded variation have been studied by quite a few authors, no simple necessary and sufficient conditions guaranteeing compactness linear integral acting such spaces known. The aim paper is to fully characterize class kernels which generate compact BV-space. Using this characterization we show that certain weakly singular convolution (such as...

A basic sequence in a Banach space is called wide-(s) if it is bounded and dominates the summing basis. (Wide-(s) sequences were originally introduced by I. Singer, who termed them P ∗-sequences.) These sequences and their quantified versions, termed λ-wide-(s) sequences, are used to characterize various classes of operators between Banach spaces, such as the weakly compact, Tauberian, and supe...

The Banach space E has the weakly compact approximation property (W.A.P. for short) if there is a constant C < ∞ so that for any weakly compact set D ⊂ E and ε > 0 there is a weakly compact operator V : E → E satisfying supx∈D ‖x − V x‖ < ε and ‖V ‖ ≤ C. We give several examples of Banach spaces both with and without this approximation property. Our main results demonstrate that the James-type ...

We study a class of left-invertible operators which we call weakly concave operators. It includes the and some subclasses expansive strict $m$ -isometries with $m &gt; 2$ . prove Wold-type decomposition for also obtain Berger–Shaw-type theorem analytic finitely cyclic The proofs these results rely heavily on spectral dichotomy provides fairly close relationship, written in terms reciprocal auto...

we investigate the problem of the existence of a frame forright ideals of a c*-algebra a, without the use of the kasparov stabilizationtheorem. we show that this property can not characterize a as a c*-algebraof compact operators.

It is shown that on certain Banach spaces, including C[0,1] and L1[0,1], there is no strongly continuous semigroup (Tt )0<t<1 consisting of weakly compact operators such that (Tt )0<t<1 is an R-bounded family. More general results concerning approximating sequences are included and some variants of R-boundedness are also discussed.  2004 Elsevier Inc. All rights reserved.