Displaying similar documents to “Linearity in non-linear problems.”

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?

The controlled separable projection property for Banach spaces

Jesús Ferrer, Marek Wójtowicz (2011)

Open Mathematics

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Let X, Y be two Banach spaces. We say that Y is a quasi-quotient of X if there is a continuous operator R: X → Y such that its range, R(X), is dense in Y. Let X be a nonseparable Banach space, and let U, W be closed subspaces of X and Y, respectively. We prove that if X has the Controlled Separable Projection Property (CSPP) (this is a weaker notion than the WCG property) and Y is a quasi-quotient of X, then the structure of Y resembles the structure of a separable Banach space: (a)...

Operators on spaces of analytic functions

K. Seddighi (1994)

Studia Mathematica

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Let M z be the operator of multiplication by z on a Banach space of functions analytic on a plane domain G. We say that M z is polynomially bounded if M p C p G for every polynomial p. We give necessary and sufficient conditions for M z to be polynomially bounded. We also characterize the finite-codimensional invariant subspaces and derive some spectral properties of the multiplication operator in case the underlying space is Hilbert.

Universal images of universal elements

Luis Bernal-González (2000)

Studia Mathematica

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We furnish several necessary and sufficient conditions for the following property: For a topological space X, a continuous selfmapping S of X and a family τ of continuous selfmappings of X, the image under S of every τ-universal element is also τ-universal. An application in operator theory, where we extend results of Bourdon, Herrero, Bes, Herzog and Lemmert, is given. In particular, it is proved that every hypercyclic operator on a real or complex Banach space has a dense invariant...