Related papers: Frequently hypercyclic bilateral shifts
Recently, the weight distributions of the duals of the cyclic codes with two zeros have been obtained for several cases. In this paper we solve one more special case. The problem of finding the weight distribution is transformed into a…
We consider a recurrent RWRE $(X_n)_{n \in \mathbb{N}_0}$ on $\mathbb{Z}$ and investigate the quenched return probabilities of the RWRE to the origin for which we state results on their decay in terms of summability. Additionally, we give…
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 obtain some results for and further examples of subprojective and superprojective Banach spaces. We also give several conditions providing examples of non-reflexive superprojective spaces; one of these conditions is stable under…
Let $A$ be a right linear operator on a two-sided quaternionic Banach space $X$. The paper studies the Drazin inverse for right linear operators on a quaternionic Banach space. It is shown that if $A$ is Drazin invertible then the Drazin…
We investigate certain envelopes of open sets in dual Banach spaces which are related to extending holomorphic functions. We give a variety of examples of absolutely convex sets showing that the extension is in many cases not possible. We…
We show that the existence of a strongly convex function with a Lipschitz derivative on a Banach space already implies that the space is isomorphic to a Hilbert space. Similarly, if both a function and its convex conjugate are $C^2$ then…
In this note, we introduce the notion of $r$-homoclinic points. We show that an operator on a Banach space is hyperbolic if and only if it is shadowing and has no nonzero $r$-homoclinic points. We also solve invariant subspace problem (ISP…
The property of being shift invariant and being reflexive or transitive in the case of the space of (asymmetric) truncated Toeplitz operators, and the space of (asymmetric) dual truncated operators is investigated. Most of the results…
In the present work we study the concepts of shadowing and chain recurrence in the setting of linear dynamics. We prove that shadowing and finite shadowing always coincide for operators on Banach spaces, but we exhibit operators on the…
This paper generalizes results for alternate dual frames in Hilbert spaces on the situation of a Banach space. Additionally some properties of synthesys operator associated with alternate dual frame are investigated. The main result is that…
It is well known that subspaces of the Hardy space over the unit disk which are invariant under the backward shift occur as the image of an observability operator associated with a discrete-time linear system with stable state-dynamics, as…
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 investigate the peripheral spectrum of irreducible positive elements of an ordered Banach algebra. In particular, we give conditions under which the peripheral spectrum contains (or coincides with) the cyclic group generated by a root of…
We provide dual sufficient conditions for subtransversality of collections of sets in an Asplund space setting. For the convex case, we formulate a necessary and sufficient dual criterion of subtransversality in general Banach spaces. Our…
We prove the existence of algebras of hypercyclic vectors in three cases: convolution operators, composition operators, and backward shift operators.
This article shows that a large class of posterior measures that are absolutely continuous with respect to a Gaussian prior have strong maximum a posteriori estimators in the sense of Dashti et al. (2013). This result holds in any separable…
We give a complete characterization of polynomials in two complex variables that are cyclic with respect to the coordinate shifts acting on Dirichlet-type spaces in the bidisk, which include the Hardy space and the Dirichlet space of the…
We consider the problem of extending an acyclic binary relation that is invariant under a given family of transformations into an invariant preference. We show that when a family of transformations is commutative, every acyclic invariant…
We provide a characterization of $J$-class and $J^{mix}$-class unilateral weighted shifts on $l^{\infty}(\mathbb{N})$ in terms of their weight sequences. In contrast to the previously mentioned result we show that a bilateral weighted shift…