Related papers: A study on coreflexive Banach Spaces

We study the group invariant continuous polynomials on a Banach space $X$ that separate a given set $K$ in $X$ and a point $z$ outside $K$. We show that if $X$ is a real Banach space, $G$ is a compact group of $\mathcal{L} (X)$, $K$ is a…

We show that a representation of a Banach algebra $A$ on a Banach space $X$ can be extended to a canonical representation of $A^{**}$ on $X$ if and only if certain orbit maps $A\to X$ are weakly compact. When this is the case, we show that…

Let $X$ and $Y$ be separable Banach spaces. Suppose $Y$ either has a shrinking basis or $Y$ is isomorphic to $C(2^\mathbb{N})$ and $A$ is a subset of weakly compact operators from $X$ to $Y$ which is analytic in the strong operator…

A topological space is said to be sequential if every sequentially closed subspace is closed. We consider Banach spaces with weak*-sequential dual ball. In particular, we show that if $X$ is a Banach space with weak*-sequentially compact…

A new method of defining hereditarily indecomposable Banach spaces is presented. This method provides a unified approach for constructing reflexive HI spaces and also HI spaces with no reflexive subspace. All the spaces presented here…

For $1\le p <\infty$, we present a reflexive Banach space $\mathfrak{X}^{(p)}_{\text{awi}}$, with an unconditional basis, that admits $\ell_p$ as a unique asymptotic model and does not contain any Asymptotic $\ell_p$ subspaces. D. Freeman,…

The purpose of this paper is to construct a new class of separable Banach spaces $\K^p[\mathbb{B}], \; 1\leq p \leq \infty$. Each of these spaces contain the $ \mcL^p[\mathbb{B}] $ spaces, as well as the space $\mfM[\R^\iy]$, of finitely…

The paper alluded to in the title contains the following striking result: Let $I$ be the unit interval and $\Delta$ the Cantor set. If $X$ is a quasi Banach space containing no copy of $c_0$ which is isomorphic to a closed subspace of a…

In this paper we investigate some reflexivity-type properties of separable measurable Banach bundles over a $\sigma$-finite measure space. Our two main results are the following: - The fibers of a bundle are uniformly convex (with a common…

We show that the problem whether every $1$-separably injective Banach space contains an isomorphic copy of $\ell_\infty$ is undecidable. Namely, unlike under the continuum hypothesis, assuming Martin's axiom and the negation of the…

Let $X$ be a Banach space with a separable dual. We prove that $X$ embeds isomorphically into a $\cL_\infty$ space $Z$ whose dual is isomorphic to $\ell_1$. If, moreover, $U$ is a space so that $U$ and $X$ are totally incomparable, then we…

The aim of the paper is to highlight some open problems concerning approximation properties of Hardy spaces. We also present some results on the bounded compact and the dual compact approximation properties (shortly, BCAP and DCAP) of such…

Let $X$ be a Banach space. For $x \in X$ with $\|x\| = 1$, we denote the state space by $S_x = \{x^* \in X^* : \|x^*\| = x^*(x) = 1\}.$ In this paper, we study weak$^*$-weak and weak$^*$-$\|\cdot\|$ points of continuity of the identity map…

A hereditarily indecomposable Banach space $\mathfrak{X}_{\mathfrak{nr}}$ is constructed that is the first known example of a $\mathscr{L}_\infty$-space not containing $c_0$, $\ell_1$, or reflexive subspaces and answers a question posed by…

We prove a commutative Gelfand--Naimark type theorem, by showing that the set $C_s(X)$ of continuous bounded (real or complex valued) functions with separable support on a locally separable metrizable space $X$ (provided with the supremum…

We present two new examples of reflexive Banach spaces $X$ for which $\mathscr{B}(X)$ is not a Grothendieck space, namely $X = T$ (the Tsirelson space) and $X = B_p$ (the $p^{\text{th}}$ Baernstein space) for $p\in(1,\infty)$.

Let $1 < p \neq q < \infty $ and $(D, \mu) = (\{\pm 1\}, 1/2 \delta_{-1} + 1/2 \delta_1)$. Define by recursion: $X_0 = \C$ and $X_{n+1} = L_p(\mu; L_q(\mu; X_n))$. In this paper, we show that there exist $c_1=c_1(p, q)>1$ depending only on…

The purpose of this article is to study the anti-coproximinal and strongly anti-coproximinal subspaces of the Banach space of all bounded (continuous) functions. We obtain a tractable necessary condition for a subspace to be stronsgly…

We construct a reflexive Banach space $X$ with a subspace isometric to $X$, which is not complemented in $X$.

A Banach space $X$ is said to have property (K) if every $w^*$-convergent sequence in $X^*$ admits a convex block subsequence which converges with respect to the Mackey topology. We study the connection of this property with strongly weakly…