Related papers: Subspaces with a common complement in a Banach spa…

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…

If a separable Banach space $X$ is such that for some nonquasireflexive Banach space $Y$ there exists a surjective strictly singular operator $T:X\to Y$ then for every countable ordinal $\alpha $ the dual of $X$ contains a subspace whose…

In this note, we consider the smallest submaximal space structure {\mu}(X) on a Banach space X. We derive a characterization of {\mu}(X) up to complete isometric isomorphism in terms of a universal property. Also, we show that an injective…

In this paper, we begin by constructing global linear maps on (n-2)-dimensional subspaces, derived from the local continuity of linear transformations among central sections of a convex body. Using these linear maps, we subsequently…

We define and study asymptotically symmetric Banach spaces (a.s.) and its variations: weakly a.s. (w.a.s.) and weakly normalized a.s. (w.n.a.s.). If X is a.s. then all spreading models of X are uniformly symmetric. We show that the converse…

We present some results related to Hahn-Banach extension theorem for linear operators on asymmetric normed spaces. L. Nachbin, Trans. Amer. Math. Soc. 68 (1950), proved that a Banach space has the extension property for linear operators (a…

It is shown that if the Deddens algebra ${\mathcal D}_T$ associated with a quasinilpotent operator $T$ on a complex Banach space is closed and localizing then $T$ has a nontrivial closed hyperinvariant subspace.

We characterize non-reflexive Banach spaces by a low-distortion (resp. isometric) embeddability of a certain metric graph up to a renorming. Also we study non-linear sufficient conditions for $\ell_1^n$ being $(1+\varepsilon)$-isomorphic to…

We study $M$-ideals of compact operators by means of the property~$(M)$ introduced in \cite{Kal-M}. Our main result states for a separable Banach space $X$ that the space of compact operators on $X$ is an $M$-ideal in the space of bounded…

We study universal approximation of continuous functionals on compact subsets of products of Hilbert spaces. We prove that any such functional can be uniformly approximated by models that first take finitely many continuous linear…

Given a finite dimensional Banach space X with dimX = n and an Auerbach basis of X, it is proved that: there exists a set D of n + 1 linear combinations (with coordinates 0, -1, +1) of the members of the basis, so that each pair of…

Assuming the generalized continuum hypothesis we construct arbitrarily big indecomposable Banach spaces. i.e., such that whenever they are decomposed as $X\oplus Y$, then one of the closed subspaces $X$ or $Y$ must be finite dimensional. It…

We prove that the following three properties for a Banach space are all different from each other: every finite convex combination of slices of the unit ball is (1) relatively weakly open, (2) has nonempty interior in relative weak topology…

If a separable Banach space contains an isometric copy of every separable reflexive Fr\'echet smooth Banach space, then it contains an isometric copy of every separable Banach space. The same conclusion holds if we consider separable Banach…

We show that operators on a separable infinite dimensional Banach space $X$ of the form $I +S$, where $S$ is an operator with dense generalised kernel, must lie in the norm closure of the hypercyclic operators on $X$, in fact in the closure…

A space $X$ is said to be hereditarily indecomposable if no two (infinite dimensional) subspaces of $X$ are in a direct sum. In this paper, we show that if $X$ is a complex hereditarily indecomposable Banach space, then every operator from…

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 prove that a Banach space has the uniform approximation property with proportional growth of the uniformity function iff it is a weak Hilbert space.

We show that if $T$ is an isometry (as metric spaces) between the invertible groups of unital Banach algebras, then $T$ is extended to a surjective real-linear isometry up to translation between the two Banach algebras. Furthermore if the…

A Banach space $X$ is said to have the Daugavet property if every operator $T: X\to X$ of rank~$1$ satisfies $\|Id+T\| = 1+\|T\|$. We show that then every weakly compact operator satisfies this equation as well and that $X$ contains a copy…