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Statements

Subject Item
n2:RIV%2F67985840%3A_____%2F13%3A00386898%21RIV13-AV0-67985840
rdf:type
skos:Concept n14:Vysledek
dcterms:description
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, it is 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. 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, it is 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.
dcterms:title
The commuting graph of bounded linear operators on a Hilbert space The commuting graph of bounded linear operators on a Hilbert space
skos:prefLabel
The commuting graph of bounded linear operators on a Hilbert space The commuting graph of bounded linear operators on a Hilbert space
skos:notation
RIV/67985840:_____/13:00386898!RIV13-AV0-67985840
n14:predkladatel
n18:ico%3A67985840
n4:aktivita
n6:P n6:I
n4:aktivity
I, P(GA201/09/0473), P(IAA100190903), P(MEB091101)
n4:cisloPeriodika
4
n4:dodaniDat
n5:2013
n4:domaciTvurceVysledku
n10:8840199 n10:5543967
n4:druhVysledku
n12:J
n4:duvernostUdaju
n17:S
n4:entitaPredkladatele
n15:predkladatel
n4:idSjednocenehoVysledku
66045
n4:idVysledku
RIV/67985840:_____/13:00386898
n4:jazykVysledku
n11:eng
n4:klicovaSlova
Hilbert space; operators; commutativity
n4:klicoveSlovo
n13:operators n13:commutativity n13:Hilbert%20space
n4:kodStatuVydavatele
US - Spojené státy americké
n4:kontrolniKodProRIV
[8BC2F54CD819]
n4:nazevZdroje
Journal of Functional Analysis
n4:obor
n19:BA
n4:pocetDomacichTvurcuVysledku
2
n4:pocetTvurcuVysledku
4
n4:projekt
n9:MEB091101 n9:GA201%2F09%2F0473 n9:IAA100190903
n4:rokUplatneniVysledku
n5:2013
n4:svazekPeriodika
264
n4:tvurceVysledku
Müller, Vladimír Ambrozie, Calin-Grigore Bračič, J. Kuzma, B.
n4:wos
000314133700007
s:issn
0022-1236
s:numberOfPages
20
n16:doi
10.1016/j.jfa.2012.11.011