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Operators admitting a closed subspace of cyclic vectors

Abstract: For an operator T acting on a complex infinite dimensional Banach space X such that T ? T is cyclic on X ? X, we show that T admits a closed infinite dimensional subspace of cyclic vectors (excluding {0}). We give some applications of this result, and we show several examples of cyclic operators T with T ?T non-cyclic admitting a closed infinite dimensional subspace of cyclic vectors.

 Fuente: Integral Equations and Operator Theory, 2018, 90(3), 28

 Editorial: Birkhauser Verlag AG

 Año de publicación: 2018

 Nº de páginas: 8

 Tipo de publicación: Artículo de Revista

 DOI: 10.1007/s00020-018-2458-2

 ISSN: 0378-620X,1420-8989

 Proyecto español: MTM2016-76958

 Url de la publicación: https://doi.org/10.1007/s00020-018-2458-2

Autoría

LEÓN SAAVEDRA, FERNANDO

ROMERO DE LA ROSA, PILAR