Related papers: A study on coreflexive Banach Spaces

The method of compatible sequences is introduced in order to produce non-trivial (closed) invariant subspaces of (bounded linear) operators. Also a topological tool is used which is new in the search of invariant subspaces: the extraction…

For any complex Banach space $X$, let $J$ denote the duality mapping of $X$. For any unit vector $x$ in $X$ and any ($C_0$) contraction semigroup $(T_t)_{t>0}$ on $X$, Baillon and Guerre-Delabriere proved that if $X$ is a smooth reflexive…

We prove that, given any covering of any separable infinite-dimensional uniformly rotund and uniformly smooth Banach space $X$ by closed balls each of positive radius, some point exists in $X$ which belongs to infinitely many balls.

In our paper [18] we showed that a Tychonoff space $X$ is a $\Delta$-space (in the sense of [20], [30]) if and only if the locally convex space $C_{p}(X)$ is distinguished. Continuing this research, we investigate whether the class $\Delta$…

Let $X$ be a Borel metric measure space such that each closed ball is of positive and finite measure. In this paper, we give a sufficient and necessary condition for averaging operators on a Banach function space $E(X)$ on $X$ to be…

We introduce a notion of p-orthogonality in a general Banach space $1 \le p \le \infty$. We use this concept to characterize $\ell_p$-spaces among Banach spaces and also among complete order smooth p-normed spaces. We further introduce a…

We prove that the spaces $\ell_p$, $1<p<\infty, p\ne 2$, and all infinite-dimensional subspaces of their quotient spaces do not admit equivalent almost transitive renormings. This is a step towards the solution of the Banach-Mazur rotation…

We consider 1-complemented subspaces (ranges of contractive projections) of vector-valued spaces $\ell_p(X)$, where $X$ is a Banach space with a 1-unconditional basis and $p \in (1,2)\cup (2,\infty)$. If the norm of $X$ is twice…

We characrterize extreme contractions defined between \ finite-dimensional polyhedral Banach spaces using $k$- smoothness of operators. We also explore weak L-P property, a recently introduced concept in the study of extreme contractions.…

In this paper we consider Meyer-Yoeurp decompositions for UMD Banach space-valued martingales. Namely, we prove that $X$ is a UMD Banach space if and only if for any fixed $p\in (1,\infty)$, any $X$-valued $L^p$-martingale $M$ has a unique…

Let $(\mathbb{X},\,d,\,\mu)$ be a space of homogeneous type in the sense of Coifman and Weiss, $X$ be a ball quasi-Banach function space on $\mathbb{X}$, $L$ be a non-negative self-adjoint operator on $L^2(\mathbb{X})$, and assume that, for…

A Banach space $X$ has the ball fixed point property (BFPP) if for every closed ball $B$ and for every nonexpansive mapping $T\colon B\to B$, there is a fixed point. We study the BFPP for $C(K)$-spaces. Our goal is to determine topological…

Let $X$ be a locally compact Hausdorff space, and $A$ be a commutative semisimple Banach algebra over the scalar field $\mathbb{C}$. The correlation between different types of BSE- Banach algebras $A$, and the Banach algebra $C_{0}(X, A)$…

We use the Gowers block Ramsey theorem to characterize Banach spaces containing isomorphs of $\ell_p$ (for some $1 \leq p < \infty$) or $c_0$.

By a result of Johnson, the Banach space $F=(\bigoplus_{n=1}^\infty \ell_1^n)_{\ell_\infty}$ contains a complemented copy of $\ell_1$. We identify $F$ with a complemented subspace of the space of (bounded, linear) operators on the reflexive…

We prove that Banach spaces $\ell_1\oplus_2\mathbb{R}$ and $X\oplus_\infty Y$, with strictly convex $X$ and $Y$, have plastic unit balls (we call a metric space plastic if every non-expansive bijection from this space onto itself is an…

In this note a large class of primary Banach spaces is characterized. Namely, it will be demonstrated that under the Continuum Hypothesis the ultrapower of any infinite dimensional nonsuperreflexive Banach space is always primary.…

Let $X$ be a complex Banach space and let $J:X \to X^*$ be a duality section on $X$ (i.e. $\langle x,J(x)\rangle=\|J(x)\|\|x\|=\|J(x)\|^2=\|x\|^2$). For any unit vector $x$ and any ($C_0$) contraction semigroup $T=\{e^{tA}:t \geq 0\}$,…

A separable Banach space X contains $\ell_1$ isomorphically if and only if X has a bounded wc_0^*-stable biorthogonal system. The dual of a separable Banach space X fails the Schur property if and only if X has a bounded wc_0^*-biorthogonal…

Let $({\mathcal X},\rho,\mu)$ be a space of homogeneous type in the sense of Coifman and Weiss, and $Y({\mathcal X})$ a ball quasi-Banach function space on ${\mathcal X}$, which supports a Fefferman--Stein vector-valued maximal inequality,…