Related papers: Saturated extensions, the attractors method and He…
In this note, we construct a distal expansion for the structure $(\mathbb{R}; +,<,H)$, where $H\subseteq \mathbb{R}$ is a dense $\mathbb{Q}$-vector space basis of $\mathbb{R}$ (a so-called Hamel basis). Our construction is also an expansion…
In this paper we study the reflexivity of a unital strongly closed algebra of operators with complemented invariant subspace lattice on a Banach space. We prove that if such an algebra contains a complete Boolean algebra of projections of…
We provide bounds on the upper box-counting dimension of negatively invariant subsets of Banach spaces, a problem that is easily reduced to covering the image of the unit ball under a linear map by a collection of balls of smaller radius.…
Can polynomial interpolation be extended to a Banach space setting? Are tensors whose elements are non-commutative Banach space elements legitimate objects with notable analytic and algebraic properties? Here we explore these questions and…
We describe the spectrum of weighted $d$-isomorphisms of Banach lattices restricted on closed subspaces that are "rich" enough to preserve some "memory" of the order structure of the original lattice. The examples include (but are not…
In this paper structure of infinite dimensional Banach spaces is studied by using an asymptotic approach based on stabilization at infinity of finite dimensional subspaces which appear everywhere far away. This leads to notions of…
This is the second part in a series dealing with subspaces of de Branges spaces of entire function generated by majorization on subsets of the closed upper half-plane. In this part we investigate certain Banach spaces generated by…
There exists a real hereditarily indecomposable Banach space $X$ such that the quotient space $L(X)/S(X)$ by strictly singular operators is isomorphic to the complex field (resp. to the quaternionic division algebra). Up to isomorphism, the…
In this survey, we present several results related to characterizing the surjective isometries on Banach sequence spaces. Our survey includes full proofs of these characterizations for the classical spaces as well as more recent results for…
In this paper we settle in the negative the problem of the superreflexivity of Garling sequence spaces by showing that they contain a complemented subspace isomorphic to a non superreflexive mixed-norm sequence space. As a by-product of our…
We consider a Hilbert space that is a product of a finite number of Hilbert spaces and operators that are represented by "componental operators" acting on the Hilbert spaces that form the product space. We attribute operatorial properties…
We construct a family $(\mathcal{X}_\al)_{\al\le \omega_1}$ of reflexive Banach spaces with long transfinite bases but with no unconditional basic sequences. In our spaces $\mathcal{X}_\al$ every bounded operator $T$ is split into its…
We study Banach spaces satisfying some geometric or structural properties involving tightness of transfinite sequences of nested linear subspaces. These properties are much weaker than WCG and closely related to Corson's property (C). Given…
We establish complete characterizations of various notions of expansivity for weighted composition operators on a very general class of locally convex spaces of continuous functions. This class includes several classical classes of…
We study composition operators on the weighted Banach spaces of an infinite tree. We characterize the bounded and the compact operators, as well as determine the operator norm and the essential norm. In addition, we study the isometric…
Let $k$ be a local field with valuation ring $O_k$ and residue field $\overline{k}$. We extend Hahn--Banach theorem for the class of seminormed $k$-vector spaces to several classes of locally convex spaces and subspaces over $k$, $O_k$, and…
In three previous papers, we discussed quasidense multifunctions from a Banach space into its dual, or, equivalently, quasidense subsets of the product of a Banach space and its dual. In this paper, we survey (without proofs) some of the…
If $X$ is a separable infinite dimensional Banach space, we construct a bounded and linear operator $R$ on $X$ such that $$ A_R=\{x \in X, \|R^tx\| \rightarrow \infty\} $$ is not dense and has non empty interior with the additional property…
We study the generic behavior of the method of successive approximations for set-valued mappings in Banach spaces. We consider, in particular, the case of those set-valued mappings which are defined by pairs of nonexpansive mappings and…
We extend and generalize the result of Kalton and Swanson ($Z_2$ is a symplectic Banach space with no Lagrangian subspace) by showing that all higher order Rochgberg spaces $\mathfrak R^{(n)}$ are symplectic Banach spaces with no Lagrangian…