The commuting graph of bounded linear operators on a Hilbert space

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F13%3A00386898" target="_blank" >RIV/67985840:_____/13:00386898 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1016/j.jfa.2012.11.011" target="_blank" >http://dx.doi.org/10.1016/j.jfa.2012.11.011</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.jfa.2012.11.011" target="_blank" >10.1016/j.jfa.2012.11.011</a>

Jazyk výsledku

angličtina

Název v původním jazyce

The commuting graph of bounded linear operators on a Hilbert space

Popis výsledku v původním jazyce

An operator T on the separable infinite-dimensional Hilbert space is constructed so that the commutant of every operator which is not a scalar multiple of the identity operator and commutes with T coincides with the commutant of T. On the other hand, itis shown that for several classes of operators it is possible to construct a finite sequence of operators, starting at a given operator from the class and ending in a rank-one projection such that each operator in the sequence commutes with its predecessor. The classes which we study are: finite-rank operators, normal operators, partial isometries, and C0 contractions. It is also shown that for any given set of yes/no conditions between points in some finite set, there always exist operators on a finite-dimensional Hilbert space such that their commutativity relations exactly satisfy those conditions.

Název v anglickém jazyce

The commuting graph of bounded linear operators on a Hilbert space

Popis výsledku anglicky

An operator T on the separable infinite-dimensional Hilbert space is constructed so that the commutant of every operator which is not a scalar multiple of the identity operator and commutes with T coincides with the commutant of T. On the other hand, itis shown that for several classes of operators it is possible to construct a finite sequence of operators, starting at a given operator from the class and ending in a rank-one projection such that each operator in the sequence commutes with its predecessor. The classes which we study are: finite-rank operators, normal operators, partial isometries, and C0 contractions. It is also shown that for any given set of yes/no conditions between points in some finite set, there always exist operators on a finite-dimensional Hilbert space such that their commutativity relations exactly satisfy those conditions.

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

Výsledek vznikl pri realizaci vícero projektů. Více informací v záložce Projekty.

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2013

Kód důvěrnosti údajů

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

Název periodika

Journal of Functional Analysis

ISSN

0022-1236

e-ISSN

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Svazek periodika

264

Číslo periodika v rámci svazku

4

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

20

Strana od-do

1068-1087

Kód UT WoS článku

000314133700007

EID výsledku v databázi Scopus

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