Results 11 to 20 of about 45 (38)

Topological Transitivity of Shift Similar Operators on Nonseparable Hilbert Spaces

Journal of Function Spaces, Volume 2021, Issue 1, 2021., 2021
In this paper, we investigate topological transitivity of operators on nonseparable Hilbert spaces which are similar to backward weighted shifts. In particular, we show that abstract differential operators and dual operators to operators of multiplication in graded Hilbert spaces are similar to backward weighted shift operators.
Andriy Zagorodnyuk, Zoriana Novosad, Ismat Beg   +2 more
wiley   +1 more source

Generalized Asymptotically Almost Periodic and Generalized Asymptotically Almost Automorphic Solutions of Abstract Multiterm Fractional Differential Inclusions

Abstract and Applied Analysis, Volume 2018, Issue 1, 2018., 2018
The main aim of this paper is to investigate generalized asymptotical almost periodicity and generalized asymptotical almost automorphy of solutions to a class of abstract (semilinear) multiterm fractional differential inclusions with Caputo derivatives. We illustrate our abstract results with several examples and possible applications.
G. M. N’Guérékata, Marko Kostić, Khalil Ezzinbi   +2 more
wiley   +1 more source

S‐Mixing Tuple of Operators on Banach Spaces

Journal of Function Spaces, Volume 2016, Issue 1, 2016., 2016
We consider the question: what is the appropriate formulation of Godefroy‐Shapiro criterion for tuples of operators? We also introduce a new notion about tuples of operators, S‐mixing, which lies between mixing and weakly mixing. We also obtain a sufficient condition to ensure a tuple of operators to be S‐mixing.
Wei Wang, Yonglu Shu, Xingzhong Wang, Enrique Llorens-Fuster   +3 more
wiley   +1 more source

Hypercyclic Behavior of Translation Operators on Spaces of Analytic Functions on Hilbert Spaces

Journal of Function Spaces, Volume 2015, Issue 1, 2015., 2015
We consider special Hilbert spaces of analytic functions of many infinite variables and examine composition operators on these spaces. In particular, we prove that under some conditions a translation operator is bounded and hypercyclic.
Zoryana Mozhyrovska, Andriy V. Zagorodnyuk, Eva A. Gallardo Gutiérrez   +2 more
wiley   +1 more source

Subspace-diskcyclic sequences of linear operators [PDF]

Sahand Communications in Mathematical Analysis, 2017
A sequence ${T_n}_{n=1}^{infty}$ of bounded linear  operators on a separable infinite dimensional Hilbert space $mathcal{H}$ is called subspace-diskcyclic with respect to the closed subspace $Msubseteq mathcal{H},$ if there exists a vector $xin mathcal{H}
Mohammad Reza Azimi
doaj  

An Extension of Hypercyclicity for N‐Linear Operators

Abstract and Applied Analysis, Volume 2014, Issue 1, 2014., 2014
Grosse‐Erdmann and Kim recently introduced the notion of bihypercyclicity for studying the existence of dense orbits under bilinear operators. We propose an alternative notion of orbit for N‐linear operators that is inspired by difference equations. Under this new notion, every separable infinite dimensional Fréchet space supports supercyclic N‐linear ...
Juan Bès, J. Alberto Conejero, Manuel Maestre   +2 more
wiley   +1 more source

The Strong Disjoint Blow‐Up/Collapse Property

Journal of Function Spaces, Volume 2013, Issue 1, 2013., 2013
Let X be a topological vector space, and let ℬ(X) be the algebra of continuous linear operators on X . The operators T1, …, TN ∈ ℬ(X) are disjoint hypercyclic if there is x ∈ X such that the orbit {(T1n(x),…,TNn(x)):n∈ℕ} is dense in X × …×X . Bès and Peris have shown that if T1, …, TN satisfy the Disjoint Blow‐up/Collapse property, then they are ...
Héctor N. Salas, Ajda Fošner
wiley   +1 more source

On the Existence of Polynomials with Chaotic Behaviour

Journal of Function Spaces, Volume 2013, Issue 1, 2013., 2013
We establish a general result on the existence of hypercyclic (resp., transitive, weakly mixing, mixing, frequently hypercyclic) polynomials on locally convex spaces. As a consequence we prove that every (real or complex) infinite‐dimensional separable Frèchet space admits mixing (hence hypercyclic) polynomials of arbitrary positive degree.
Nilson C. Bernardes Jr., Alfredo Peris, Ajda Fošner   +2 more
wiley   +1 more source

Frequently Hypercyclic and Chaotic Behavior of Some First‐Order Partial Differential Equation

Abstract and Applied Analysis, Volume 2013, Issue 1, 2013., 2013
We study a particular first‐order partial differential equation which arisen from a biologic model. We found that the solution semigroup of this partial differential equation is a frequently hypercyclic semigroup. Furthermore, we show that it satisfies the frequently hypercyclic criterion, and hence the solution semigroup is also a chaotic semigroup.
Cheng-Hung Hung, Yu-Hsien Chang, Josef Diblík   +2 more
wiley   +1 more source

Devaney Chaos and Distributional Chaos in the Solution of Certain Partial Differential Equations

Abstract and Applied Analysis, Volume 2012, Issue 1, 2012., 2012
The notion of distributional chaos has been recently added to the study of the linear dynamics of operators and C0‐semigroups of operators. We will study this notion of chaos for some examples of C0‐semigroups that are already known to be Devaney chaotic.
Xavier Barrachina, J. Alberto Conejero, Elena Litsyn   +2 more
wiley   +1 more source