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We study topological groups of monotonic autohomeomorphisms on a generalized ordered space $L$. We find a condition that is necessary and sufficient for the set of all monotonic autohomeomorphisms on $L$ along with the function composition…
Given a pair $(M,X)$, where $X$ is a smooth submanifold in a closed smooth manifold $M$, we study the operation, which takes each operator $D$ on the ambient manifold to a certain operator on the submanifold. The latter operator is called…
We consider sequences of operators $U_n:L^1(X)\to M(X)$, where $X$ is a space of homogeneous type. Under certain conditions on the operators $U_n$ we give a complete characterization of convergence (divergence) sets of functional sequences…
We introduce and study the notion of orthosymmetric spaces over an Archimedean vector lattice as a generalization of finite-dimentional Euclidean inner spaces. A special attention has been paid to linear operators on these spaces.
Frequent hypercyclicity for translation $C_0$-semigroups on weighted spaces of continuous functions is investigated. The results are achieved by establishing an analogy between frequent hypercyclicity for the translation semigroup and for…
Let $S$ be a finitely generated abelian semigroup of invertible linear operators on a finite dimensional real or complex vector space $V$. We show that every coarsely dense orbit of $S$ is actually dense in $V$. More generally, if the orbit…
In this work we shall prove new results on the theory of convolution operators on spaces of entire functions. The focus is on hypercyclicity results for convolution operators on spaces of entire functions of a given type and order; and…
We define a new version of Topological Complexity (TC) of a space, denoted as $\text{dTC}$, which, we think, fits better for motion planning for some autonomous systems. Like Topological complexity, \text{dTC} is also a homotopy invariant.…
An explicit construction of all the homogeneous holomorphic Hermitian vector bundles over the unit disc $\mathbb D$ is given. It is shown that every such vector bundle is a direct sum of irreducible ones. Among these irreducible homogeneous…
The stochastic generators of Markov-regular operator cocycles on symmetric Fock space are studied in a variety of cases: positive cocycles, projection cocycles, and partially isometric cocycles. Moreover a class of transformations of…
We study the topology of circularly ordered sets. While the algebraic notion is classical, the general topological theory has received comparatively little attention. In this work we provide a self-contained topological exposition and…
We describe the orbit structure for the action of the centralizer group of a linear operator on a finite-dimensional complex vector space. The main application is to the classification of solutions to a system of first-order ODEs with…
We study continuity and boundedness of order-to-topology bounded and order-to topology continuous operators from ordered to topological vector spaces. Several results on automatic continuity of operators from ordered Frechet spaces to…
In this paper, we define in an intrinsic way operators on a compact Lie group by means of symbols using the representations of the group. The main purpose is to show that these operators form a symbolic pseudo-differential calculus which…
Let $G$ be a connected, real semisimple Lie group. Let $K<G$ be maximal compact, and let $\Gamma < G$ be discrete and such that $\Gamma \backslash G$ has finite volume. If the real rank of $G$ is $1$ and $\Gamma$ is torsion-free, then…
Let $X$ be an Archimedean vector lattice. We investigate subalgebras of $\mathscr{L}(X)$ consisting of regular operators that contain all rank-one operators of the form $a \otimes \varphi_b$, where $a$ and $b$ are atoms of $X$ and…
We investigate spaceability phenomena in linear dynamics from a structural perspective. Given a continuous linear operator \(T:X \to X\), we introduce the set \(\Omega(T)\), consisting of all continuous linear operators \(h:X \to X\) for…
The introduction of the categorical notion of closure operators has unified various important notions and has led to interesting examples and applications in diverse areas of mathematics (see for example, Dikranjan and Tholen (\cite{DT})).…
It is proved that, if $(P_n)$ is a sequence of polynomials with complex coefficients having unbounded valences and tending to infinity at sufficiently many points, then there is an infinite dimensional closed subspace of entire functions,…
This paper is devoted to the study of typical properties (in the Baire Category sense) of certain classes of continuous linear operators acting on Fr\'echet algebras, endowed with the topology of pointwise convergence. Our main results show…