On orbit-reflexive operators

0341043 - MÚ 2010 RIV GB eng J - Journal Article
Müller, Vladimír - Vršovský, Jan
On orbit-reflexive operators.
Journal of the London Mathematical Society. Roč. 79, č. 2 (2009), s. 497-510. ISSN 0024-6107. E-ISSN 1469-7750
Institutional research plan: CEZ:AV0Z10190503
Keywords : reflexive operators * orbit-reflexivity
Subject RIV: BA - General Mathematics
Impact factor: 0.798, year: 2009

Let T be a bounded linear Banach space operator such that P∞ n=1 1 kTnk <∞. Then T is orbit-reflexive. In particular, every Banach space operator with spectral radius different from 1 is orbit-reflexive. Better estimates are obtained for operators in Hilbert spaces. We also exhibit a simple example of a non-orbit-reflexive Hilbert space operator and an example of a reflexive but non-orbit-reflexive operator (acting on ℓ1).
Permanent Link: http://hdl.handle.net/11104/0184152