$BANCH banach

Latest papers

1. Compactness and weak compactness of linearized Holomorphic-Lipschitz maps math.FA · 19 Oct · 2 hits

   Any holomorphic Lipschitz map $f$, defined on the open unit ball $B_X$ of a complex Banach space $X$ and taking values in a complex Banach space $Y$, can be uniquely and canonically associated…

2. Approximation numbers of critical Besov embeddings math.FA · 19 Oct · 1 hit

   …inner indices follow from Malykhin's finite-window estimates and norm comparisons. The results include quasi-Banach indices and the full spaces of bounded coefficient sequences at infinite fine indices.

3. Geometric and measure-theoretic characterizations of the measure-determining property of balls in metric spaces math.FA · 19 Oct · 1 hit

   …been known since the 1970s, and it was shown by Preiss and Ti\v{s}er (1991) that it holds for all separable Banach spaces, Davies (1971) constructed a famous counterexample that shows it can fail on compact metric…

4. Operators commuting with $L^\infty$]{Operators commuting with $L^\infty$ on K\"othe--Bochner spaces math.FA · 17 Oct · 2 hits

   Let $E(X)$ be a K\"othe--Bochner space of functions on a $\sigma$-finite measure space with values in a Banach space $X$. We study bounded operators on $E(X)$ that commute with the operators of multiplication by…

5. Extension of surjective isometries between unit spheres of $\ell^p$-direct sums math.FA · 17 Oct · 1 hit

   We study surjective isometries between the unit spheres of Banach spaces of the form $A\oplus_p B$, where $A$ is nonzero and strictly convex, $1<p<\infty$, and every…

6. On condensations of $C_p(X)$ spaces onto Banach spaces with the weak topology math.FA · 16 Oct · 3 hits

   …on $X$ equipped with the pointwise topology maps bijectively onto any separable infinite-dimensional Banach space with the weak topology. We prove that the inverse $\varphi^{-1}$ of any continuous bijection…

7. Strongly Choquet-Deny groups and invariant strictly convex renormings math.FA · 16 Oct · 2 hits

   …is strongly Choquet-Deny if and only if for every uniformly bounded representation of $G$ on any separable Banach space $X$, there exists an equivalent $G$-invariant strictly convex norm on $X$. We provide a full…

8. Weak$^*$-weak points of continuity and very smooth points in Bochner function spaces $L^{p}(\mu, X)$ math.FA · 16 Oct · 1 hit

   …point of continuity of $S(X^*)$ for almost every $t\in [0, 1]$ with $h(t)\neq 0$, where $X$ is a Banach space such that $X^*$ is separable. As an application of this result, under the same hypothesis on…