Results 1 to 10 of about 45 (32)
Some necessary and sufficient conditions for Hypercyclicity Criterion [PDF]
Proceedings of the Indian Academy of Sciences: Mathematical Sciences, 2005 We give necessary and sufficient conditions for an operator on a separable Hilbert space to satisfy the hypercyclicity criterion.
H Rezaei, Yousefi B, B Yousefi
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The Hypercyclicity Criterion for sequences of operators [PDF]
Studia Mathematica, 2003 Let \(X\) denote a separable, complete, metrizable topological vector space (a separable \(F\)-space). A sequence \((T_n) \subset L(X)\) of continuous linear operators on \(X\) is called hypercyclic if there exists \(x \in X\), called a hypercyclic vector, for the sequence, such that its orbit \(\{ T_1(x),T_2(x),\dots \}\) is dense in \(X\). A sequence
L Bernal-González
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Hypercyclic operators failing the Hypercyclicity Criterion on classical Banach spaces
Journal of Functional Analysis, 2007 Let \(X\) be a topological vector space over \(\mathbb{R}\) or \(\mathbb{C}\). A (continuous, linear) operator \(T:X \to X\) is said to be hypercyclic if there exists some \(x \in X\) whose \(T\)-orbit \(\{T^n x: n\in{\mathbb{N}}\}\) is dense in \(X\). In [J.~Funct.~Anal.\ 99, 179--190 (1991; Zbl 0758.47016)], \textit{D.\,Herrero} posed the problem of ...
E Matheron
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A hypercyclicity criterion with applications
Journal of Mathematical Analysis and Applications, 2007 The following hypercyclicity criterion for continuous linear operators \(T: X \rightarrow X\) defined on a Hausdorff locally convex space \((X,\tau)\) is proved: Assume that \(X\) admits a finer topology \(\mu\) such that \((X,\mu)\) is a Fréchet space and \(T\) is \(\mu\)-continuous. Suppose that there is a countable \(\tau\)-dense subset \(Y\) of \(X\
Henrik Petersson
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A probabilistic version of the Frequent Hypercyclicity Criterion [PDF]
Studia Mathematica, 2006 For a bounded operator T on a separable infinite-dimensional Banach space X, we give a "random" criterion not involving ergodic theory which implies that T is frequently hypercyclic: there exists a vector x such that for every non-empty open subset U of X, the set of integers n such that Tnx belongs to U, has positive lower density ...
Sophie Grivaux
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TUPLE OF OPERATORS WITH THE PROPERTY OF HYPERCYCLICITY CRITERION [PDF]
International Journal of Pure and Applied Mathematics, 2013 Summary: In this paper, we give conditions under which a tuple of operators satisfies the Hypercyclicity Criterion.
B Yousefi
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Journal of Mathematical Analysis and Applications, 2014 Let \(T_1,\dots,T_N\) be bounded, linear operators on a separable infinite-dimensional Banach space \(X\). According to \textit{L. Bernal-González} [Stud. Math. 182, No. 2, 113--131 (2007; Zbl 1134.47006)], \textit{J. Bès} and \textit{A. Peris} [J. Math. Anal. Appl. 336, No.
Stanislav Shkarin, Rebecca Sanders
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Hypercyclicity Criterion on Basic Elementary Operator
Journal of Advances in Mathematics and Computer ScienceHypercyclicity criterion has been an important tool in the test of hypercyclicity of different operators. This tool has been used by different mathematicians to show that generalized derivations, left and right multiplication operators, operator algebra and backward shift operators are hypercyclic.
Kawira Esther +2 more
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THE $M$-HYPERCYCLICITY CRITERION OF $C_{0}$-SEMIGROUPS [PDF]
International Journal of Pure and Applied Mathematics, 2017 A. Tajmouati, A. El Bakkali, A. Toukmati
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About Subspace-Frequently Hypercyclic Operators [PDF]
Sahand Communications in Mathematical Analysis, 2020 In this paper, we introduce subspace-frequently hypercyclic operators. We show that these operators are subspace-hypercyclic and there are subspace-hypercyclic operators that are not subspace-frequently hypercyclic. There is a criterion like to subspace-
Mansooreh Moosapoor, Mohammad Shahriari
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