Related papers: Hypercyclicity, existence and approximation result…

We describe cyclic vectors for a Pommiez operator on a weighted (LF)-space E of entire functions. The full description is obtained where $E$ is the Laplace transform of the strong dual of the space of all germs of holomorphic functions on a…

In this paper, we answer a question posed in the introduction of \cite{sub hyp} positively, i.e, we show that if $T$ is $\mathcal M$-hypercyclic operator with $\mathcal M$-hypercyclic vector $x$ in a Hilbert space $\mathcal H$, then…

Let $T$ be an absolutely continuous polynomially bounded operator, and let $\theta$ be a singular inner function. It is shown that if $\theta(T)$ is invertible and some additional conditions are fulfilled, then $T$ has nontrivial…

We investigate operators between spaces of holomorphic functions in several complex variables. Let $G_1, G_2 \subset \mathbb{C}^n$ be cylindrical domains. We construct a canonical map from the space of bounded linear operators…

This tutorial paper presents a survey of results, both classical and new, linking inner functions and operator theory. Topics discussed include invariant subspaces, universal operators, Hankel and Toeplitz operators, model spaces, truncated…

This paper deals with eigenvalues and eigenvectors of bicomplex linear operators defined on bicomplex space. We investigate the properties of these operators in the context of eigenvalues and eigenvectors, along with some relevant theorems.…

In this paper we establish a new equivalence relation on the spaces of almost periodic functions which allows us to prove a result like Bohr's equivalence theorem extended to the case of all these functions.

Estimating the coefficient functionals on various classes of holomorphic functions traditionally forms an important field of geometric complex analysis and its mathematical and physical applications. These coefficients reflect fundamental…

Let $\mathcal{H}$ be an infinite dimensional real or complex separable Hilbert space. We introduce a special type of a bounded linear operator $T$ and its important relation with invariant subspace problem on $\mathcal{H}$: operator $T$ is…

This survey on approximations of perturbed operator functions addresses recent advances and some of the successful methods.

We summarise recent work on superconformal field theories using analytic superspace. All operators of N=4 SYM can be given as unconstrained superfields on analytic superspace. We show how to write down operators as superfields on analytic…

Let T and C be two Hilbert space operators. We prove that if T is near, in a certain sense, to an operator completely polynomially dominated with a finite bound by C, then T is similar to an operator which is completely polynomially…

We study hypercyclicity of Toeplitz operators in the Hardy space $H^2(\mathbb{D})$ with symbols of the form $R(\overline{z}) +\phi(z)$, where $R$ is a rational function and $\phi \in H^\infty(\mathbb{D})$. We relate this problem to…

We show that for any uniformly parabolic fully nonlinear second-order equation with bounded measurable "coefficients" and bounded "free" term in the whole space or in any cylindrical smooth domain with smooth boundary data one can find an…

Operator convex functions defined on the positive half-line play a prominent role in the theory of quantum information, where they are used to define quantum $f$-divergences. Such functions admit integral representations in terms of…

We show that for every supercyclic strongly continuous operator semigroup ${T_t}_{t\geq 0}$ acting on a complex $\F$-space, every $T_t$ with $t>0$ is supercyclic. Moreover, the set of supercyclic vectors of each $T_t$ with $t>0$ is exactly…

We explore boundedness properties in the context of metric measure spaces, of some natural operators of convolution type whose study is suggested by certain transformations used in computer vision.

We introduce and study the notion of hereditary frequent hypercyclicity, which is a reinforcement of the well known concept of frequent hypercyclicity. This notion is useful for the study of the dynamical properties of direct sums of…

All continuous, SL$(n)$ and translation invariant valuations on the space of convex functions on ${\mathbb R}^n$ are completely classified.

New perspectives, proofs, and some extensions of known results are presented concerning the behavior of the Fitzpatrick function of a monotone type operator in the general context of a locally convex space.