Chaotic extensions of operators on Hilbert subspaces

If M is a closed subspace of a separable, infinite dimensional Hilbert space H with dim ( H / M ) = ∞, we show that every bounded linear operator A : M → M can be extended to a chaotic operator T : H → H that satisfies the hypercyclicity criterion in the strongest possible sense.

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Veröffentlicht in:	Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A, Matemáticas Físicas y Naturales. Serie A, Matemáticas, 2011-09, Vol.105 (2), p.415-421
Hauptverfasser:	Chan, Kit C., Turcu, G.
Format:	Artikel
Sprache:	eng
Schlagworte:	Applications of Mathematics Chaos theory Criteria Hilbert space Linear operators Mathematical and Computational Physics Mathematics Mathematics and Statistics Operators Subspaces Theoretical
Online-Zugang:	Volltext
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Beschreibung
Zusammenfassung:	If M is a closed subspace of a separable, infinite dimensional Hilbert space H with dim ( H / M ) = ∞, we show that every bounded linear operator A : M → M can be extended to a chaotic operator T : H → H that satisfies the hypercyclicity criterion in the strongest possible sense.
ISSN:	1578-7303 1579-1505
DOI:	10.1007/s13398-011-0029-3