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Operator Machines on Directed Graphs
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SYSNO ASEP 0352530 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title Operator Machines on Directed Graphs Author(s) Hájek, Petr Pavel (MU-W) RID, SAI
Smith, R.J. (GB)Source Title Integral Equations and Operator Theory - ISSN 0378-620X
Roč. 67, č. 1 (2010), s. 15-31Number of pages 17 s. Language eng - English Country CH - Switzerland Keywords orbits of operators Subject RIV BA - General Mathematics R&D Projects IAA100190801 GA AV ČR - Academy of Sciences of the Czech Republic (AV ČR) CEZ AV0Z10190503 - MU-W (2005-2011) UT WOS 000277097100002 EID SCOPUS 77951877585 DOI 10.1007/s00020-010-1766-y Annotation 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. Workplace Mathematical Institute Contact Jarmila Štruncová, struncova@math.cas.cz, library@math.cas.cz, Tel.: 222 090 757 Year of Publishing 2011
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