On orbit-reflexive operators

0341043 - MÚ 2010 RIV GB eng J - Článek v odborném periodiku
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
Výzkumný záměr: CEZ:AV0Z10190503
Klíčová slova: reflexive operators * orbit-reflexivity
Kód oboru RIV: BA - Obecná matematika
Impakt faktor: 0.798, rok: 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).
Trvalý link: http://hdl.handle.net/11104/0184152