Criteria for compactly locally uniformly rotund points in Orlicz spaces are given.

We show that the Hilbert space is coarsely embeddable into any ${\ell }_p$ for 1 ≤ p ≤ ∞. It follows that coarse embeddability into ℓ₂ and into ${\ell }_p$ are equivalent for 1 ≤ p < 2.

Let X be a complex Banach space and let Bloch(X) denote the space of X-valued analytic functions on the unit disc such that $su{p}_{\left|z\right|<1}(1-|z\left|²\right)\left|\right|f^{\text{'}}\left(z\right)\left|\right|<\infty$. A sequence (Tₙ)ₙ of bounded operators between two Banach spaces X and Y is said to be an operator-valued multiplier between Bloch(X) and ℓ₁(Y) if the map ${\sum }_{n=0}^{\infty }xₙzⁿ\to \left(Tₙ\left(xₙ\right)\right)ₙ$ defines a bounded linear operator from Bloch(X) into ℓ₁(Y). It is shown that if X is a Hilbert space then (Tₙ)ₙ is a multiplier from Bloch(X) into ℓ₁(Y) if and only if $su{p}_k{\sum }_{n=2^k}^{2^{k+1}}\left|\right|Tₙ\left|\right|²<\infty$. Several results about Taylor coefficients of vector-valued...

We are concerned with a relation between parabolicity and coerciveness in Besov spaces for a higher order linear evolution equation in a Banach space. As proved in a preceding work, a higher order linear evolution equation enjoys coerciveness in Besov spaces under a certain parabolicity condition adopted and studied by several authors. We show that for a higher order linear evolution equation coerciveness in Besov spaces forces the parabolicity of the equation. We thus conclude that parabolicity...

Various proofs of the Factorization Theorem for representations of Banach algebras are compared with its original proof due to P. Cohen.

Suppose that A and B are unital Banach algebras with units $1_A$ and $1_B$, respectively, M is a unital Banach A,B-module, $=\left[\begin{array}{cc}A& M\\ 0& B\end{array}\right]$ is the triangular Banach algebra, X is a unital -bimodule, $X_{AA}=1_{A}X{1}_A$, $X_{BB}=1_{B}X{1}_B$, $X_{AB}=1_{A}X{1}_B$ and $X_{BA}=1_{B}X{1}_A$. Applying two nice long exact sequences related to A, B, , X, $X_{AA}$, $X_{BB}$, $X_{AB}$ and $X_{BA}$ we establish some results on (co)homology of triangular Banach algebras.

R. Deville and J. Rodríguez proved that, for every Hilbert generated space $X$, every Pettis integrable function $f:[0,1]\to X$ is McShane integrable. R. Avilés, G. Plebanek, and J. Rodríguez constructed a weakly compactly generated Banach space $X$ and a scalarly null (hence Pettis integrable) function from $[0,1]$ into $X$, which was not McShane integrable. We study here the mechanism behind the McShane integrability of scalarly negligible functions from $[0,1]$ (mostly) into $C\left(K\right)$ spaces. We focus in more detail on the behavior...