Počet záznamů: 1

Operator Machines on Directed Graphs

  1. 1.
    0352530 - MU-W 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
    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
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