Different versions of Wiener’s Tauberian theorem are discussed for the generalized group algebra LI(G,A) (of integrable functions on a locally compact abelian group G taking values in a commutative semisimple regular Banach algebra A) using A-valued Fourier transforms. A weak form of Wiener’s Tauberian property is introduced and it is proved that LI(G,A) is weakly Tauberian if and only if A is....

The purpose of this paper is to establish some weak convergence theorems of modified two-step iteration process with errors for two asymptotically quasi-nonexpansive non-self mappings in the setting of real uniformly convex Banach spaces if E satisfies Opial’s condition or the dual E∗ of E has the Kedec-Klee property. Our results extend and improve some known corresponding results from the exis...

We prove that if a metric probability space with a usual concentration property embeds into a finite dimensional Banach space X , then X has a Euclidean subspace of a proportional dimension. In particular this yields a new characterization of weak cotype 2. We also find optimal lower estimates on embeddings of metric spaces with concentration properties into l ∞, generalizing estimates of Bourg...

We study the class of separable (real) Banach spaces X which can be embedded into a space C(K) (K compact metric) in only one way up to automorphism. We show that in addition to the known spaces c0 (and all it subspaces) and 1 (and all its weak∗-closed subspaces) the space c0( 1) has this property. We show on the other hand (answering a question of Castillo and Moreno) that p for 1< p <∞ fails ...

Dowling et al. in 1 defined a norm in l1 which was used by Lin 2 to exhibit an equivalent norm which makes l1 into a space with the fixed point property FPP . A similar norm can be defined in every Banach spaceX with a basis. Since l1 with its usual norm does not have FPP, we asked ourselves if this norm in these spaces would also improve properties that imply the weak fixed point property WFPP...

• Banach-Alaoglu: compactness of polars • Variant Banach-Steinhaus/uniform boundedness • Second polars • Weak boundedness implies boundedness • Weak-to-strong differentiability The comparison of weak and strong differentiability is due to Grothendieck, although the original sources are not widely available.

In this paper by using some conditions, we show that the weak amenability of (2n)-th dual of a Banach algebra A for some $ngeq 1$ implies the weak amenability of A.