Related papers: Reflexive Calkin algebras

For $1<p\le \infty$, we show the existence of a Banach space which is both injectively and surjectively universal for the class of all separable Banach spaces with an equivalent $p$-asymptotically uniformly smooth norm. We prove that this…

Let $L$ be an elliptic differential operator with bounded measurable coefficients, acting in Bochner spaces $L^{p}(R^{n};X)$ of $X$-valued functions on $R^n$. We characterize Kato's square root estimates $\|\sqrt{L}u\|_{p} \eqsim \|\nabla…

We construct a hereditarily indecomposable Banach space with dual isomorphic to $\ell_1$. Every bounded linear operator on this space has the form $\lambda I+K$ with $\lambda$ a scalar and $K$ compact.

We exhibit a Banach space $Z$ failing the approximation property, for which there is an uncountable family $\mathscr F$ of closed subideals contained in the Banach algebra $\mathcal K(Z)$ of the compact operators on $Z$, such that the…

We show that for any separable reflexive Banach space $X$ and a large class of Banach spaces $E$, including those with a subsymmetric shrinking basis but also all spaces $L_p$ for $1\leq p \leq \infty$, every bounded linear map ${\mathcal…

We provide a complete description of those Banach algebras that are generated by an invertible isometry of an $L^p$-space together with its inverse. Examples include the algebra $PF_p(\mathbb{Z})$ of $p$-pseudofunctions on $\mathbb{Z}$, the…

In this article, we give a representation for compact operators acting between reflexive Banach spaces, which generalizes the representation given by Edmunds et al. for compact operators between reflexive Banach spaces with strictly convex…

In this paper, by dilation technique on Schauder frames, we extend Godefroy and Kalton's approximation theorem (1997), and obtain that a separable Banach space has the $\lambda$-unconditional bounded approximation property ($\lambda$-UBAP)…

We define the notion of isometric envelope of a subspace in a Banach space, and relate it to a) the mean ergodic projection on the space of fixed points of a semigroup of contractions, b) results on Korovkin sets from the 70's, and c)…

A Banach space $X$ is elastic if there is a constant $K$ so that whenever a Banach space $Y$ embeds into $X$, then there is an embedding of $Y$ into $X$ with constant $K$. We prove that $C[0,1]$ embeds into separable infinite dimensional…

Given a Boolean algebra $A$, we construct another Boolean algebra $B$ with no uncountable well-ordered chains such that the Banach space of real valued continuous functions $C(K_A)$ embeds isometrically into $C(K_B)$, where $K_A$ and $K_B$…

We characterize Hilbert spaces in the class of all Banach spaces using Fourier transform of vector-valued functions over the field $Q_p$ of $p$-adic numbers. Precisely, Banach space $X$ is isomorphic to a Hilbert one if and only if Fourier…

We show that any Banach space contains a continuum of non isomorphic subspaces or a minimal subspace. We define an ergodic Banach space $X$ as a space such that $E_0$ Borel reduces to isomorphism on the set of subspaces of $X$, and show…

Let $X$ be a reflexive Banach space such that for any $x \ne 0$ the set $$ \{x^* \in X^*: \text {$\|x^*\|=1$ and $x^*(x)=\|x\|$}\} $$ is compact. We prove that any unrestricted product of of a finite number of $(W)$ contractions on $X$…

If $X$ is a compact Hausdorff space and $\sigma$ is a homeomorphism of $X$, then a Banach algebra $\ell^1(\Sigma)$ of crossed product type is naturally associated with this topological dynamical system $\Sigma=(X,\sigma)$. If $X$ consists…

In this paper we study the ideal amenability of Banach algebras. Let $\cal A$ be a Banach algebra and let $I$ be a closed two-sided ideal in $\cal A$, $\cal A$ is $I$-weakly amenable if $H^{1}({\cal A},I^*)=\{0\}$. Further, $\cal A$ is…

We give a new proof of a recent characterization by Diaz and Mayoral of compactness in the Lebesgue-Bochner spaces $L_X^p$, where $X$ is a Banach space and $1\le p<\infty$, and extend the result to vector-valued Banach function spaces…

We study the complexities of isometry and isomorphism classes of separable Banach spaces in the Polish spaces of Banach spaces recently introduced and investigated by the authors in [14]. We obtain sharp results concerning the most…

Let $X$, $Y$ be two real Banach spaces and $\varepsilon>0$. A standard $\varepsilon$-isometry $f:X\rightarrow Y$ is said to be $(\alpha,\gamma)$-stable (with respect to $T:L(f)\equiv\overline{{\rm span}}f(X)\rightarrow X$ for some $\alpha,…

Let $E$ be one of the spaces $C(K)$ and $L_1$, $F$ be an arbitrary Banach space, $p>1,$ and $(X,\sigma)$ be a space with a finite measure. We prove that $E$ is isometric to a subspace of the Lebesgue-Bochner space $L_p(X;F)$ only if $E$ is…