Related papers: Typical properties of positive contractions and th…

In this article, we address a problem posed by F. Bayart regarding the existence of an infinite-dimensional closed vector subspace (excluding the null operator) within the set of supercyclic operators on Banach spaces. We resolve this…

We study the invertibility of Banach algebras elements in their extensions, and invertible extensions of Banach and Hilbert space operators with prescribed growth conditions for the norm of inverses. As applications, the solutions of two…

We establish new results on the $\mathcal I$-approximation property for the Banach operator ideal $\mathcal I=\mathcal{K}_{up}$ of the unconditionally $p$-compact operators in the case of $1\le p<2$. As a consequence of our results, we…

Let $E$ and $G$ be two Banach function spaces, let $T \in \mathcal{L}(E,Y)$, and let ${\langle X,Y \rangle}$ be a Banach dual pair. In this paper we give conditions for which there exists a (necessarily unique) bounded linear operator…

We study the spaceability of the set of recurrent vectors $\text{Rec}(T)$ for an operator $T:X\longrightarrow X$ on a Banach space $X$. In particular: we find sufficient conditions for a quasi-rigid operator to have a recurrent subspace;…

Let $\mathcal H$ be an infinite-dimensional Hilbert space, and let $\mathcal B(\mathcal H)$ ($\mathcal K(\mathcal H)$) be the $C^*$-algebra of bounded (respectively, compact) linear operators in $\mathcal H$. Let $(E,\|\cdot\|_E)$ be a…

We show that for any bounded operator $T$ acting on infinite dimensional, complex Banach space, and for any $\varepsilon>0$, there exists an operator $F$ of rank at most one and norm smaller than $\varepsilon$ such that $T+F$ has an…

We investigate M-ideals of compact operators and two distinct properties in norm-attaining operator theory related with M-ideals of compact operators called the weak maximizing property and the compact perturbation property. For Banach…

For an unbounded operator $S$ on a Banach space the existence of invariant subspaces corresponding to its spectrum in the left and right half-plane is proved. The general assumption on $S$ is the uniform boundedness of the resolvent along…

A bounded linear operator $T$ on a Banach space $X$ is called frequently hypercyclic if there exists $x\in X$ such that the lower density of the set $\{n\in\N:T^nx\in U\}$ is positive for any non-empty open subset $U$ of $X$. Bayart and…

In this paper, we use the Mordukhovich derivatives to precisely find the covering constants for the metric projection operator onto nonempty closed and convex subsets in uniformly convex and uniformly smooth Banach spaces. We consider three…

In this paper, we investigate the invertibility of $I_Y+\delta TT^+$ when $T$ is a closed operator from $X$ to $Y$ with a generalized inverse $T^+$ and $\delta T$ is a linear operator whose domain contains $D(T)$ and range is contained in…

We explore extreme contractions between finite-dimensional polygonal Banach spaces, from the point of view of attainment of norm of a linear operator. We prove that if $ X $ is an $ n- $dimensional polygonal Banach space and $ Y $ is any…

We consider weak-star closed invariant subspaces of the shift operator in the classical Bloch space. We prove that any bounded analytic function decomposes into two factors, one which is cyclic and another one generating a proper shift…

If $T$ is a polynomially bounded operator, $\mathcal M$ is an invariant subspace of $T$, $T|_{\mathcal M}$ is a unilateral shift and $T^*|_{\mathcal M^\perp}$ is subnormal, then $T$ has a nontrivial hyperinvariant subspace. If an operator…

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…

In this paper, we establish the one-sided maximal ergodic inequalities for a large subclass of positive operators on noncommutative $L_p$-spaces for a fixed $1<p<\infty$, which particularly applies to positive isometries and general…

Fixed point theory studies conditions under which nonexpansive maps on Banach spaces have fixed points. This paper examines the open question of whether every reflexive Banach space has the fixed point property. After surveying classical…

Our aim in this paper is to present a new type of the modular space. This space contains the classical modular space. There are some mappings that do not have contractive condition in the usual modular space but become contraction in this…

Let $T$ be a bounded linear operator on a Banach space $X$ satisfying $\|T^n\|/n \to 0$. We prove that $T$ is uniformly ergodic if and only if the one-sided ergodic Hilbert transform $H_Tx:= \lim_{n\to\infty} \sum_{k=1}^n k^{-1}T^k x$…