Results 1 to 10 of about 32 (27)

Hereditarily Hypercyclic Operators [PDF]

Journal of Functional Analysis, 1999
We show that a continuous linear operator T on a Fréchet space satisfies the so-called Hypercyclicity Criterion if and only if it is hereditarily hypercyclic, and if and only if the direct sum T⊕T is hypercyclic. In particular, hypercyclic operators with
Alfred Peris, Juan Bes
exaly   +2 more sources

Convolution operators and the discrete Laplacian [PDF]

, 2009
PhDIn this thesis, we obtain new results for convolution operators on homogeneous spaces and give applications to the Laplacian on a homogeneous graph. Some of these results have been published in joint papers [13, 14] with my supervisor.
Chen, Chung-Chuan
core   +4 more sources

Operators with dense, invariant, cyclic vector manifolds [PDF]

, 1991
We study a class of Banach space operators patterned after the weighted backward shifts on Hilbert space, and show that any non-scalar operator in the commutant of one of these “generalized backward shifts” has a dense, invariant linear manifold whose ...
Godefroy, Gilles, Shapiro, Joel H
core   +1 more source

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

Dynamics, Operator Theory, and Infinite Holomorphy

, 2014
Abstract and Applied Analysis, Volume 2014, Issue 1, 2014.
Alfred Peris, Manuel Maestre, Miguel Martín, Yun Sung Choi   +3 more
wiley   +1 more source

On Some Subspace Codiskcyclic Operators in Banach Spaces

International Journal of Mathematics and Mathematical Sciences, Volume 2025, Issue 1, 2025.
This paper introduces the concepts of subspace codiskcyclicity and subspace codisk transitivity, providing criteria and examples that highlight their distinct properties compared to traditional codiskcyclic operators and hypercyclic operators. The paper also demonstrates the existence of subspace codiskcyclic operators in finite‐dimensional Banach ...
Peter Masong Slaa, Santosh Kumar, Marco Mpimbo, Shikha Binwal   +3 more
wiley   +1 more source

Numerically hypercyclic operators

, 2012
An operator T acting on a normed space E is numerically hypercyclic if, for some (x, x*) is an element of Pi(E), the numerical orbit {x*(T-n(x)) : n >= 0} is dense in C.
Song, Hyun Gwi, Peris Manguillot, Alfredo, Kim, Sung Guen   +2 more
core   +1 more source

Frequently Hypercyclic Semigroup Generated by Some Partial Differential Equations with Delay Operator

Abstract and Applied Analysis, Volume 2024, Issue 1, 2024.
In this paper, under appropriate hypotheses, we have the existence of a solution semigroup of partial differential equations with delay operator. These equations are used to describe time–age‐structured cell cycle model. We also prove that the solution semigroup is a frequently hypercyclic semigroup.
Cheng-Hung Hung, Victor Kovtunenko
wiley   +1 more source

Numerically hypercyclic polynomials

, 2012
In this paper, we show that every complex Banach space X with dimension at least 2 supports a numerically hypercyclic d-homogeneous polynomial P for every . Moreover, if X is infinite-dimensional, then one can find hypercyclic non-homogeneous polynomials
Song, Hyun Gwi, Peris Manguillot, Alfredo, Kim, Sung Guen   +2 more
core   +1 more source

Hypercyclic Translation Operators on the Algebra of Compact Operators

Iranian Journal of Science and Technology Transaction A: Science, 2021
Seyyed Mohammad Tabatabaie
exaly