Related papers: Frequently recurrence properties and block familie…
Considering a family of upper frequently hypercyclic operators we care about the existence of vectors which are upper frequently hypercyclic for any operator of this family. We establish sufficient conditions for a family of operators to…
Given a family of subspaces we investigate existence, quantity and quality of common complements in Hilbert spaces and Banach spaces. In particular we are interested in complements for countable families of closed subspaces of finite…
In this paper, we analyze recurrent $C_{0}$-semigroups of bounded operators on Banach spaces. We also introduce the notion of a (uniformly) $C_{0}$-rigid semigroups of bounded operators and give a structural characterization of them. A…
We study ordinal-indexed, multi-layer iterations of bounded operator transforms and prove convergence to spectral/ergodic projections under functional-calculus hypotheses. For normal operators on Hilbert space and polynomial or holomorphic…
We study Li-Yorke chaos and distributional chaos for operators on Banach spaces. More precisely, we characterize Li-Yorke chaos in terms of the existence of irregular vectors. Sufficient "computable" criteria for distributional and Li-Yorke…
We present partial results to the following question: Does every infinite dimensional Banach space have an infinite dimensional subspace on which one can define an operator which is not a compact perturbation of a scalar multiplication?
We show that there exist infinite-dimensional extremely non-complex Banach spaces, i.e. spaces $X$ such that the norm equality $\|Id + T^2\|=1 + \|T^2\|$ holds for every bounded linear operator $T:X\longrightarrow X$. This answers in the…
If a separable Banach space $X$ is such that for some nonquasireflexive Banach space $Y$ there exists a surjective strictly singular operator $T:X\to Y$ then for every countable ordinal $\alpha $ the dual of $X$ contains a subspace whose…
Although recurrence for dynamical systems has been studied since the end of the nineteenth century, the study of recurrence for linear operators started with papers by Costakis, Manoussos and Parissis in 2012 and 2014. We explore recurrence…
In this note we discuss an open problem whether a truncated Toeplitz operator on a model space can be hypercyclic. We compute point spectrum and eigenfunctions for a class of truncated Toeplitz operators with polynomial analytic and…
Quasi-one-dimensional stochastic Dirac operators with an odd number of channels, time reversal symmetry but otherwise efficiently coupled randomness are shown to have one conducting channel and absolutely continuous spectrum of multiplicity…
Given any continuous self-map f of a Banach space E over K (where K is R or C) and given any point p of E, we define a subset sigma(f,p) of K, called spectrum of f at p, which coincides with the usual spectrum sigma(f) of f in the linear…
It is introduced an open class of linear operators on Banach and Hilbert spaces such that their non-wandering set is an infinite dimensional topologically mixing subspace. In certain cases, the non-wandering set coincides with the whole…
Given a Banach space X and a bounded linear operator T on X, a subspace Y of X is almost invariant under T if TY is a subspace of Y+F for some finite-dimensional ``error'' F. In this paper, we study subspaces that are almost invariant under…
In this work, we prove that linear bounded operators $T$ on a Banach space $X$ allowing spectral cuts along rectifiable Jordan curves meeting their spectrum are related to classes of operators admitting an unconventional functional…
We prove that any Boolean algebra with the subsequential completeness property contains an independent family of size continuum. This improves a result of Argyros from the 80ties which asserted the existence of an uncountable independent…
We consider a family of operators $-\Delta+ t V$ with a slowly decaying and oscillating potential $V$. We prove that the absolutely continuous spectrum of this operator is essentially supported by $[0,\infty)$ for almost every $t$.
Let $T$ be a positive operator on a complex Banach lattice. It is a long open problem whether the peripheral spectrum $\sigma_{\operatorname{per}}(T)$ of $T$ is always cyclic. We consider several growth conditions on $T$, involving its…
Fenchel subdifferential operators of lower semicontinuous proper convex functions on real Banach spaces are classically characterized as those operators that are maximally cyclically monotone or, equivalently, maximally monotone and…
We use the method of atomic decomposition and a new family of Banach spaces to study the action of transfer operators associated to piecewise-defined maps. It turns out that these transfer operators are quasi-compact even when the…