Displaying similar documents to “On operators T such that f(T) is hypercyclic.”

Hypercyclic sequences of operators

Fernando León-Saavedra, Vladimír Müller (2006)

Studia Mathematica

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A sequence (Tₙ) of bounded linear operators between Banach spaces X,Y is said to be hypercyclic if there exists a vector x ∈ X such that the orbit Tₙx is dense in Y. The paper gives a survey of various conditions that imply the hypercyclicity of (Tₙ) and studies relations among them. The particular case of X = Y and mutually commuting operators Tₙ is analyzed. This includes the most interesting cases (Tⁿ) and (λₙTⁿ) where T is a fixed operator and λₙ are complex numbers. We also study...

Recent developments in hypercyclicity.

Karl-Goswin Grosse-Erdmann (2003)

RACSAM

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In these notes we report on recent progress in the theory of hypercyclic and chaotic operators. Our discussion will be guided by the following fundamental problems: How do we recognize hypercyclic operators? How many vectors are hypercyclic? How many operators are hypercyclic? How big can non-dense orbits be?

n-supercyclic operators

Nathan S. Feldman (2002)

Studia Mathematica

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We show that there are linear operators on Hilbert space that have n-dimensional subspaces with dense orbit, but no (n-1)-dimensional subspaces with dense orbit. This leads to a new class of operators, called the n-supercyclic operators. We show that many cohyponormal operators are n-supercyclic. Furthermore, we prove that for an n-supercyclic operator, there are n circles centered at the origin such that every component of the spectrum must intersect one of these circles.

Disjoint hypercyclic operators

Luis Bernal-González (2007)

Studia Mathematica

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We introduce the concept of disjoint hypercyclic operators. These are operators performing the approximation of any given vectors with a common subsequence of iterates applied on a common vector. The notion is extended to sequences of operators, and applied to composition operators and differential operators on spaces of analytic functions.

Intertwining Multiplication Operators on Function Spaces

Bahman Yousefi, Leila Bagheri (2006)

Bulletin of the Polish Academy of Sciences. Mathematics

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Suppose that X is a Banach space of analytic functions on a plane domain Ω. We characterize the operators T that intertwine with the multiplication operators acting on X.

Dense range perturbations of hypercyclic operators

Luis Bernal-Gonzalez (2002)

Colloquium Mathematicae

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We show that if (Tₙ) is a hypercyclic sequence of linear operators on a locally convex space and (Sₙ) is a sequence of linear operators such that the image of each orbit under every linear functional is non-dense then the sequence (Tₙ + Sₙ) has dense range. Furthermore, it is proved that if T,S are commuting linear operators in such a way that T is hypercyclic and all orbits under S satisfy the above non-denseness property then T - S has dense range. Corresponding statements for operators...

Narrow operators and rich subspaces of Banach spaces with the Daugavet property

Vladimir M. Kadets, Roman V. Shvidkoy, Dirk Werner (2001)

Studia Mathematica

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Let X be a Banach space. We introduce a formal approach which seems to be useful in the study of those properties of operators on X which depend only on the norms of the images of elements. This approach is applied to the Daugavet equation for norms of operators; in particular we develop a general theory of narrow operators and rich subspaces of spaces X with the Daugavet property previously studied in the context of the classical spaces C(K) and L₁(μ).

The Positive Supercyclicity Theorem.

F. León Saavedra (2004)

Extracta Mathematicae

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We present some recent results related with supercyclic operators, also some of its consequences. We will finalize with new related questions.