The Hypercyclicity Criterion for sequences of operators

By L. Bernal-Gonz'alez, K. Grosse-Erdmann. 2003

73 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Applied Mathematics

View Paper: https://www.semanticscholar.org/paper/5e909cfb23b0702c65418d592edfc70f32defcf9

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In Algebra and Number Theory

In Applied Mathematics

Citations in the corpus

Universal functions for composition operators with non-automorphic symbol (2009, background): “Now, in the theory of universality a sequence of operators is called hereditarily universal (or hereditarily hypercyclic) if each of its subsequences is universal, see [6].”
HYPERCYCLIC OPERATORS, MIXING OPERATORS AND THE BOUNDED STEPS PROBLEM (2005, background): “That (i) implies (ii) is obvious, and the converse has been proved by Bernal-Gonzalez and Grosse-Erdmann in [8].”
On hypercyclicity and supercyclicity criteria (2004, result): “F-space) was given by Received 14th October, 2003 The authors' would like to thank Luis Bernal and Karl Grosse-Erdmann who informed us about the coincidence of some of their results with ours in Section 2, gave us a copy of their paper [5], and finally made some interesting comments about our articl”
Linear subsets of nonlinear sets in topological vector spaces (2013, background): “It can be proved (see [81] and [90]) that, for separable F-spaces X and Y , the sequence (Tn) satisfies the UC if and only if some subsequence of it is hereditarily densely universal.”
Disjointness in hypercyclicity (2007, methodology): “The next definition is adapted from the so-called Hypercyclicity Criterion, due to Kitai [19] and to Gethner and Shapiro [11]; see also [4,5] and [13].”
Hypercyclic weighted translations on groups (2011, result): “Hypercyclic operators have been studied by many authors; we refer to [2, 3, 5, 7, 9, 11, 12, 16, 17, 18] for some recent works.”