A continuous model for quasinilpotent operators

Gallardo-Gutiérrez, E.A. ; Partington, J.R. ; Rodríguez, D.J.

Resumen: A classical result due to Foias and Pearcy establishes a discrete model for every quasinilpotent operator acting on a separable, infinite-dimensional complex Hilbert space (Formula presented.). More precisely, given a quasinilpotent operator T on (Formula presented.), there exists a compact quasinilpotent operator K in (Formula presented.) such that T is similar to a part of (Formula presented.) acting on the direct sum of countably many copies of (Formula presented.). We show that a continuous model for any quasinilpotent operator can be provided. The consequences of such a model will be discussed in the context of (Formula presented.)-semigroups of quasinilpotent operators.

Idioma: Inglés

DOI: 10.1007/s00209-016-1673-2

Año: 2016

Publicado en: MATHEMATISCHE ZEITSCHRIFT (2016), 1-10
ISSN: 0025-5874

Factor impacto JCR: 0.738 (2016)

Categ. JCR: MATHEMATICS rank: 123 / 310 = 0.397 (2016) - Q2 - T2

Factor impacto SCIMAGO: 1.691 - Mathematics (miscellaneous) (Q1)

Financiación: info:eu-repo/grantAgreement/ES/MINECO/EEBB-I-14-08134

Tipo y forma: Article (Published version)