Operator Machines on Directed Graphs

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F10%3A00352530" target="_blank" >RIV/67985840:_____/10:00352530 - isvavai.cz</a>

Result on the web

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DOI - Digital Object Identifier

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Result language

angličtina

Original language name

Operator Machines on Directed Graphs

Original language description

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.

Czech name

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Czech description

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Type

J_x - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)

CEP classification

BA - General mathematics

OECD FORD branch

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Project

<a href="/en/project/IAA100190801" target="_blank" >IAA100190801: Smoothness in Banach spaces</a><br>

Continuities

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>Z - Vyzkumny zamer (s odkazem do CEZ)

Publication year

2010

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

Integral Equations and Operator Theory

ISSN

0378-620X

e-ISSN

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Volume of the periodical

67

Issue of the periodical within the volume

1

Country of publishing house

CH - SWITZERLAND

Number of pages

17

Pages from-to

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UT code for WoS article

000277097100002

EID of the result in the Scopus database

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