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Audiovisual Mathematics Library

Audiovisual Mathematics Library

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Spectral decompositions and an extension of a theorem of Atzmon: a couple leading to spectral subspaces for Bishop operators - Gallardo-Gutiérrez, Eva A. (Author of the conference) | CIRM H

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Bishop's operator arose in the fifties as possible candidates for being counterexamples to the Invariant Subspace Problem. Several authors addressed the problem of finding invariant subspaces for some of these operators; but still the general problem is open. In this talk, we shall discuss about recent results on the existence of invariant subspaces which are indeed spectral subspaces for Bishop operators, by providing an extension of a Theorem of Atzmon (Joint work with M. Monsalve-Lopez).[-]
Bishop's operator arose in the fifties as possible candidates for being counterexamples to the Invariant Subspace Problem. Several authors addressed the problem of finding invariant subspaces for some of these operators; but still the general problem is open. In this talk, we shall discuss about recent results on the existence of invariant subspaces which are indeed spectral subspaces for Bishop operators, by providing an extension of a Theorem ...[+]

47A15 ; 47B37 ; 47B38

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How to shift from frequent hypercyclicity to chaos? - Menet, Quentin (Author of the conference) | CIRM H

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In linear dynamics, chaos requires the density of some orbits and the density of periodic points while frequent hypercyclicity assumes the existence of orbits visiting frequently each non-empty open set. These two notions that we thought were linked are not in general. However, neither are they completely foreign to each other and in particular when we consider the most studied operators in linear dynamics: weighted shifts.

47A16 ; 47B37 ; 46A45

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