Počet záznamů: 1
Operator Machines on Directed Graphs
- 1.0352530 - MÚ 2011 RIV CH eng J - Článek v odborném periodiku
Hájek, Petr Pavel - Smith, R.J.
Operator Machines on Directed Graphs.
Integral Equations and Operator Theory. Roč. 67, č. 1 (2010), s. 15-31. ISSN 0378-620X. E-ISSN 1420-8989
Grant CEP: GA AV ČR IAA100190801
Výzkumný záměr: CEZ:AV0Z10190503
Klíčová slova: orbits of operators
Kód oboru RIV: BA - Obecná matematika
Impakt faktor: 0.521, rok: 2010
http://link.springer.com/article/10.1007%2Fs00020-010-1766-y
We show that if an infinite-dimensional Banach space X has a symmetric basis then there exists a bounded, linear operator R : X -> X such that the set A = {x is an element of X : parallel to R(n)x parallel to -> infinity} is non-empty and nowhere norm-dense in X. Moreover, if x is an element of X/A then some subsequence of (R-n x)(n=1)(infinity) converges weakly to x. This answers in the negative a recent conjecture of Prajitura. The result can be extended to any Banach space containing an infinite-dimensional, complemented subspace with a symmetric basis; in particular, all 'classical' Banach spaces admit such an operator.
Trvalý link: http://hdl.handle.net/11104/0192020
Název souboru Staženo Velikost Komentář Verze Přístup Hajek4.pdf 1 260.9 KB Vydavatelský postprint vyžádat
Počet záznamů: 1