Related papers: On the minimal number of matrices which form a loc…

Each symmetrically-normed ideal $\mathcal{I}$ of compact operators on a Hilbert space $H$ induces a multiplier topology $\mu^*_{\mathcal{I}}$ on the algebra $\mathcal{B}(H)$ of bounded operators. We show that under fairly reasonable…

We consider a family of $2 \times 2$ operator matrices ${\mathcal A}_\mu(k),$ $k \in {\Bbb T}^3:=(-\pi, \pi]^3,$ $\mu>0$, acting in the direct sum of zero- and one-particle subspaces of a Fock space. It is associated with the Hamiltonian of…

A bounded linear operator $T$ on a Banach space $X$ is called subspace-hypercyclic if there is a subspace $M \subsetneq X$ and a vector $x \in X$ such that $orb{(x,T)} \cap M$ is dense in $M$. We show that every Banach space supports…

Frames formed by orbits of vectors through the iteration of a bounded operator have recently attracted considerable attention, in particular due to its applications to dynamical sampling. In this article, we consider two commuting bounded…

In this paper we establish hypercyclicity of continuous linear operators on $H(\mathbb{C})$ that satisfy certain commutation relations.

We treat some questions related to supercyclicity of continuous linear operators when acting in locally convex spaces. We extend results of Ansari and Bourdon and consider doubly power bounded operators in this general setting. Some…

In the present article, we investigate a possibility of a real-valued map on the space of tuples of commuting trace-class self-adjoint operators, which behaves like the usual trace map on the space of trace-class linear operators. It turns…

We show that for sufficiently large $n$, every 3-uniform hypergraph on $n$ vertices with minimum vertex degree at least $\binom{n-1}2 - \binom{\lfloor\frac34 n\rfloor}2 + c$, where $c=2$ if $n\in 4\mathbb{N}$ and $c=1$ if $n\in…

Motivated by classical nontransitivity paradoxes, we call an $n$-tuple $(x_1,\dots,x_n) \in[0,1]^n$ \textit{cyclic} if there exist independent random variables $U_1,\dots, U_n$ with $P(U_i=U_j)=0$ for $i\not=j$ such that…

We characterize the strictly increasing symbols $\varphi:\mathbb{N}_0\longrightarrow\mathbb{N}_0$ whose composition operators $C_{\varphi}$ satisfy the Frequent Hypercyclicity Criterion on the little Lipschitz space…

It has been recently shown that $|| F_n(A) ||\leq 2$, where $A$ is a linear continuous operator acting in a Hilbert space, and $F_n$ is the Faber polynomial of degree $n$ corresponding to some convex compact $E\subset \mathbb C$ containing…

In this note, it is proved the existence of an infinitely generated multiplicative group consisting of entire functions that are, except for the constant function 1, hypercyclic with respect to the convolution operator associated to a given…

Let (k(n)) n=1,2,... be a strictly increasing sequence of positive integers . We consider a specific sequence of differential operators Tk(n),{\lambda} , n=1,2,... on the space of entire functions , that depend on the sequence (k(n))…

For fields with more than $2$ elements, the classification of the vector spaces of matrices with rank at most $2$ is already known. In this work, we complete that classification for the field $\mathbb{F}_2$. We apply the results to obtain…

We study the trace set of the commutator subgroup of $\Gamma(2),$ a type of Local-Global problem about thin groups. We determine the local obstructions and then use the correspondence between binary quadratic forms and hyperbolic matrices…

Our aim is to study topological minimality of some natural matrix groups. We show that the special upper triangular group $SUT(n,\mathbb{F})$ is minimal for every local field $\mathbb{F}$ of characteristic $\neq 2$. This result is new even…

The problem of classifying tuples of nilpotent matrices over a field under simultaneous conjugation is considered "hopeless". However, for any given matrix order over a finite field, the number of concerned orbits is always finite. This…

Using works of T.~Ando and L.~Gurvits, the well-known theorem of P.R.~Halmos concerning the existence of unitary dilations for contractive linear operators acting on Hilbert spaces recast as a result for $d$-tuples of contractive Hilbert…

We show that Voiculescu's circular operator and, more generally, each circular free Poisson operator has a continuous family of invariant subspaces relative to the von Neumann algebra it generates. The proof relies on upper triangular…

We give an analogue for vertex operator algebras and superalgebras of the notion of endomorphism ring of a vector space by means of a notion of ``local system of vertex operators'' for a (super) vector space. We first prove that any local…