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On orbit‐reflexive operators
Author(s) -
Müller V.,
Vršovský J.
Publication year - 2009
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/jdn081
Subject(s) - mathematics , bounded operator , reflexive operator algebra , hilbert space , reflexivity , operator (biology) , operator space , spectral radius , pure mathematics , finite rank operator , orbit (dynamics) , bounded function , banach space , pseudo monotone operator , reflexive space , compact operator , mathematical analysis , computer science , physics , interpolation space , quantum mechanics , functional analysis , chemistry , eigenvalues and eigenvectors , social science , repressor , aerospace engineering , sociology , engineering , biochemistry , transcription factor , programming language , extension (predicate logic) , gene
Let T be a bounded linear Banach space operator such that∑ n = 1 ∞ 1 / | | T n | | < ∞. Then T is orbit‐reflexive. In particular, every Banach space operator with a spectral radius different from 1 is orbit‐reflexive. Better estimates are obtained for operators in Hilbert spaces. We also present a simple example of a nonorbit‐reflexive Hilbert space operator and an example of a reflexive but nonorbit‐reflexive operator (acting on ℓ 1 ).