منابع مشابه
Hypercyclic Behaviour of Operators in a Hypercyclic C0-Semigroup
Let {Tt}t≥0 be a hypercyclic strongly continuous semigroup of operators. Then each Tt (t > 0) is hypercyclic as a single operator, and it shares the set of hypercyclic vectors with the semigroup. This answers in the affirmative a natural question concerning hypercyclic C0-semigroups. The analogous result for frequent hypercyclicity is also obtained.
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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-hypercyclicity criterion that implies subspace-frequent hypercyclicity and if an operator $T$ satisfies this criterion, then $Toplus T$ is sub...
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We provide a reasonable sufficient condition for a family of operators to have a common hypercyclic subspace. We also extend a result of the third author and A. Montes [22], thereby obtaining a common hypercyclic subspace for certain countable families of compact perturbations of operators of norm no larger than one.
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We prove that, given a sequence of points in a complex domain Ω without accumulation points, there are functions having prescribed values at the points of the sequence and, simultaneously, having dense orbit in the space of holomorphic functions on Ω . The orbit is taken with respect to any fixed nonscalar differential operator generated by an entire function of subexponential type, thereby ext...
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We provide a criterion for the existence of a residual set of common hypercyclic vectors for an uncountable family of hypercyclic operators, which is based on a previous one given by Costakis and Sambarino. As an application, we get common hypercyclic vectors for a particular family of hypercyclic scalar multiples of the adjoint of a multiplier in the Hardy space, generalizing recent results by...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2003
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-03-07016-3