Displaying similar documents to “A probabilistic version of the Frequent Hypercyclicity Criterion”

Supercyclicity in the operator algebra

Alfonso Montes-Rodríguez, M. Carmen Romero-Moreno (2002)

Studia Mathematica

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We prove a Supercyclicity Criterion for a continuous linear mapping that is defined on the operator algebra of a separable Banach space ℬ. Our result extends a recent result on hypercyclicity on the operator algebra of a Hilbert space. This kind of result is a powerful tool to analyze the structure of supercyclic vectors of a supercyclic operator that is defined on ℬ. For instance, as a consequence of the main result, we give a very simple proof of the recently established fact that...

Lineability of functionals and operators

Francisco Javier García-Pacheco, Daniele Puglisi (2010)

Studia Mathematica

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This article is divided into two parts. The first one is on the linear structure of the set of norm-attaining functionals on a Banach space. We prove that every Banach space that admits an infinite-dimensional separable quotient can be equivalently renormed so that the set of norm-attaining functionals contains an infinite-dimensional vector subspace. This partially solves a question proposed by Aron and Gurariy. The second part is on the linear structure of dominated operators. We show...

Constructing non-compact operators into c₀

Iryna Banakh, Taras Banakh (2010)

Studia Mathematica

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We prove that for each dense non-compact linear operator S: X → Y between Banach spaces there is a linear operator T: Y → c₀ such that the operator TS: X → c₀ is not compact. This generalizes the Josefson-Nissenzweig Theorem.

Mean ergodicity for compact operators

Heydar Radjavi, Ping-Kwan Tam, Kok-Keong Tan (2003)

Studia Mathematica

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A mean ergodic theorem is proved for a compact operator on a Banach space without assuming mean-boundedness. Some related results are also presented.

Linear Colligations and Dynamic System Corresponding to Operators in the Banach Space

Hatamleh, Raed (2007)

Serdica Mathematical Journal

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2000 Mathematics Subject Classification: Primary 47A48, 93B28, 47A65; Secondary 34C94. New concepts of linear colligations and dynamic systems, corresponding to the linear operators, acting in the Banach spaces, are introduced. The main properties of the transfer function and its relation to the dual transfer function are established.

The algebraic size of the family of injective operators

Luis Bernal-González (2017)

Open Mathematics

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In this paper, a criterion for the existence of large linear algebras consisting, except for zero, of one-to-one operators on an infinite dimensional Banach space is provided. As a consequence, it is shown that every separable infinite dimensional Banach space supports a commutative infinitely generated free linear algebra of operators all of whose nonzero members are one-to-one. In certain cases, the assertion holds for nonseparable Banach spaces.

Ergodic theorems for subadditive superstationary families of random sets with values in Banach spaces

G. Krupa (1998)

Studia Mathematica

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Under different compactness assumptions pointwise and mean ergodic theorems for subadditive superstationary families of random sets whose values are weakly (or strongly) compact convex subsets of a separable Banach space are presented. The results generalize those of [14], where random sets in ℝ d are considered. Techniques used here are inspired by [3].

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).

Ball remotal subspaces of Banach spaces

Pradipta Bandyopadhyay, Bor-Luh Lin, T. S. S. R. K. Rao (2009)

Colloquium Mathematicae

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We study Banach spaces X with subspaces Y whose unit ball is densely remotal in X. We show that for several classes of Banach spaces, the unit ball of the space of compact operators is densely remotal in the space of bounded operators. We also show that for several classical Banach spaces, the unit ball is densely remotal in the duals of higher even order. We show that for a separable remotal set E ⊆ X, the set of Bochner integrable functions with values in E is a remotal set in L¹(μ,X). ...

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...

Sobczyk's theorem and the Bounded Approximation Property

Jesús M. F. Castillo, Yolanda Moreno (2010)

Studia Mathematica

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Sobczyk's theorem asserts that every c₀-valued operator defined on a separable Banach space can be extended to every separable superspace. This paper is devoted to obtaining the most general vector valued version of the theorem, extending and completing previous results of Rosenthal, Johnson-Oikhberg and Cabello. Our approach is homological and nonlinear, transforming the problem of extension of operators into the problem of approximating z-linear maps by linear maps.

Deviation from weak Banach–Saks property for countable direct sums

Andrzej Kryczka (2014)

Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica

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We introduce a seminorm for bounded linear operators between Banach spaces that shows the deviation from the weak Banach–Saks property. We prove that if (Xv) is a sequence of Banach spaces and a Banach sequence lattice E has the Banach–Saks property, then the deviation from the weak Banach–Saks property of an operator of a certain class between direct sums E(Xv) is equal to the supremum of such deviations attained on the coordinates Xv. This is a quantitative version for operators of...