Related papers: Generic properties of l_p-contractions and similar…
In this article, we study the similarity of the Polish operator topologies $\texttt{WOT}$, $\texttt{SOT}$, $\texttt{SOT}\mbox{$_{*}$}$ and $\texttt{SOT}\mbox{$^{*}$}$ on the set of the positive contractions on $\ell_p$ with $p > 1$. Using…
We study some local spectral properties of contraction operators on $\ell_p$, $1<p<\infty$ from a Baire category point of view, with respect to the Strong$^*$ Operator Topology. In particular, we show that a typical contraction on $\ell_p$…
Given a Polish topology $\tau$ on ${{\mathcal{B}}_{1}(X)}$, the set of all contraction operators on $X=\ell_p$, $1\le p<\infty$ or $X=c_0$, we prove several results related to the following question: does a typical $T\in…
In this paper, we first study some elementary properties of a typical positive contraction on $\ell_q$ for the Strong Operator Topology and the Strong* Operator Topology. Using these properties, we prove that a typical positive contraction…
We show that (for the weak operator topology) the set of unitary operators on a separable infinite-dimensional Hilbert space is residual in the set of all contractions. The analogous result holds for isometries and the strong operator…
We introduce and study Polish topologies on various spaces of countable enumerated groups, where an enumerated group is simply a group whose underlying set is the set of natural numbers. Using elementary tools and well known examples from…
We study some dynamical properties of composition operators defined on the space $\mathcal{P}(^m X)$ of $m$-homogeneous polynomials on a Banach space $X$ when $\mathcal{P}(^m X)$ is endowed with two different topologies: the one of uniform…
We answer positively a question of Ryzhikov, namely we show that being a relatively weakly mixing extension is a comeager property in the Polish group of measure preserving transformations. We study some related classes of ergodic…
Let $\ell^{p}$, $1\leq p<\infty$, be the Banach space of absolutely $p$-th power summable sequences and let $\pi_{n}$ be the natural projection to the $n$-th coordinate for $n\in\mathbb{N}$. Let $\mathfrak{W}=\{w_{n}\}_{n=1}^{\infty}$ be a…
We study topological properties of conjugacy classes in Polish groups, with emphasis on automorphism groups of homogeneous countable structures. We first consider the existence of dense conjugacy classes (the topological Rokhlin property).…
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 consider $\ell^r$ extensions of Calderon-Zygmund operators on weighted spaces $L^p(w)$ with $w$ an $A_p$ weight and $1 < p < \infty$. We give quantitative estimates of these operators' norm in terms of a given weight's $A_p$…
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…
Countably infinite groups (with a fixed underlying set) constitute a Polish space $G$ with a suitable metric, hence the Baire category theorem holds in $G$. We study isomorphism invariant subsets of $G$, which we call group properties. We…
A topological setting is defined to study the complexities of the relation of equivalence of embeddings (or "position") of a Banach space into another and of the relation of isomorphism of complex structures on a real Banach space. The…
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 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.…
We study ergodicity of composition operators on rearrangement-invariant Banach function spaces. More precisely, we give a natural and easy-to-check condition on the symbol of the operator which entails mean ergodicity on a very large class…
We show that the strong operator topology, the weak operator topology and the compact-open topology agree on the space of unitary operators of a infinite dimensional separable Hilbert space. Moreover, we show that the unitary group endowed…
We present a comprehensive theory of boundedness properties for Polish groups developed with a main focus on Roelcke precompactness (precompactness of the lower uniformity) and Property (OB) (boundedness of all isometric actions on…