Related papers: On the minimal number of matrices which form a loc…
We introduce and study a class of operator tuples in complex Hilbert spaces, which we call spherical tuples. In particular, we characterize spherical multi-shifts, and more generally, multiplication tuples on RKHS. We further use these…
Two $n$-dimensional vectors $A$ and $B$, $A,B \in \mathbb{R}^n$, are said to be \emph{trivially orthogonal} if in every coordinate $i \in [n]$, at least one of $A(i)$ or $B(i)$ is zero. Given the $n$-dimensional Hamming cube $\{0,1\}^n$, we…
In this paper, we define and study subspace-diskcyclic operators. We show that subspace-diskcyclicity does not imply to diskcyclicity. We establish a subspace-diskcyclic criterion and use it to find a subspace-diskcyclic operator that is…
We provide conditions for a linear map of the form $C_{R,T}(S)=RST$ to be $q$-frequently hypercyclic on algebras of operators on separable Banach spaces. In particular, if $R$ is a bounded operator satisfying the $q$-Frequent Hypercyclicity…
The notions of weak and strong minimizability of a matrix intertwining operator are introduced. Criterion of strong minimizability of a matrix intertwining operator is revealed. Criterion and sufficient condition of existence of a constant…
We study intertwining relations for matrix one-dimensional, in general, non-Hermitian Hamiltonians by matrix differential operators of arbitrary order. It is established that for any matrix intertwining operator Q_N^- of minimal order N…
We prove the existence of algebras of hypercyclic vectors in three cases: convolution operators, composition operators, and backward shift operators.
We provide with criteria for a family of sequences of operators to share a frequently universal vector. These criteria are variants of the classical Frequent Hypercyclicity Criterion and of a recent criterion due to Grivaux, Matheron and…
We derive necessary and sufficient conditions for local unitary (LU) operators to leave invariant the set of 1-qubit reduced density matrices of a multi-qubit state. LU operators with this property are tensor products of {\it cyclic local}…
In this paper, we prove that if $T$ is diskcyclic operator then the closed unit disk multiplied by the union of the numerical range of all iterations of $T$ is dense in $\mathcal H$. Also, if $T$ is diskcyclic operator and $|\lambda|\le 1$,…
Bonet, Frerick, Peris and Wengenroth constructed a hypercyclic operator on the locally convex direct sum of countably many copies of the Banach space $\ell_1$. We extend this result. In particular, we show that there is a hypercyclic…
In this work we address the classical problem of classifying tuples of linear operators and linear functions on a finite dimensional vector space up to base change. Having adopted for the situation considered a construction of framed moduli…
In this document we study the uniform local path connectivity of sets of $m$-tuples of pairwise commuting normal matrices with some additional constraints. More specifically, given given $\varepsilon>0$, a fixed metric $\eth$ in…
Let $C$ be an algebraic curve of genus $g$ and $L$ a line bundle over $C$. Let $\mathcal{MS}_C(n,L)$ and $\mathcal{MO}_C(n,L)$ be the moduli spaces of $L$-valued symplectic and orthogonal bundles respectively, over $C$ of rank $n$. We…
An $n$-tuple of operators $(V_1,...,V_n)$ acting on a Hilbert space $H$ is said to be isometric if the operator $[V_1\...\ V_n]:H^n\to H$ is an isometry. We prove a decomposition for an isometric tuple of operators that generalizes the…
In this paper, a criterion for a sequence of composition operators defined on the space of holomorphic functions in a complex domain to be frequently hypercyclic is provided. Such criterion improves some already known special cases and, in…
Recent work in Dynamical Sampling has been centered on characterizing frames obtained by the orbit of a vector under a bounded operator. We prove a necessary and sufficient condition for a pair of bounded commuting operators on a separable…
We provide necessary and sufficient conditions on the existence of common hypercyclic vectors for multiples of the backward shift operator along sparse powers. Our main result strongly generalizes corresponding results which concern the…
A matrix is said to be {\it cyclic} if its characteristic polynomial is equal to its minimal polynomial. Cyclic matrices play an important role in some algorithms for matrix group computation, such as the Cyclic Meataxe developed by P. M.…
In this paper, we prove that the minimal number of affine maps on C^n, required to form a hypercyclic abelian semigroup on C^n is n+1. We also prove that the action of any abelian group finitely generated by affine maps on C^n, is never…