About: The commuting graph of bounded linear operators on a Hilbert space

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
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. (en)
Title	The commuting graph of bounded linear operators on a Hilbert space The commuting graph of bounded linear operators on a Hilbert space (en)
skos:prefLabel	The commuting graph of bounded linear operators on a Hilbert space The commuting graph of bounded linear operators on a Hilbert space (en)
skos:notation	RIV/67985840:_____/13:00386898!RIV13-AV0-67985840
http://linked.open...avai/predkladatel	Matematický ústav AV ČR, v. v. i.
http://linked.open...avai/riv/aktivita	I P
http://linked.open...avai/riv/aktivity	I, P(GA201/09/0473), P(IAA100190903), P(MEB091101)
http://linked.open...iv/cisloPeriodika	4
http://linked.open...vai/riv/dodaniDat	2013
http://linked.open...aciTvurceVysledku	Müller, Vladimír Ambrozie, Calin-Grigore
http://linked.open.../riv/druhVysledku	J - Článek v odborném periodiku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	Matematický ústav AV ČR, v. v. i.
http://linked.open...dnocenehoVysledku	66045
http://linked.open...ai/riv/idVysledku	RIV/67985840:_____/13:00386898
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	Hilbert space; operators; commutativity (en)
http://linked.open.../riv/klicoveSlovo	Hilbert space operators commutativity
http://linked.open...odStatuVydavatele	US - Spojené státy americké
http://linked.open...ontrolniKodProRIV	[8BC2F54CD819]
http://linked.open...i/riv/nazevZdroje	Journal of Functional Analysis
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	2 (xsd:int)
http://linked.open...cetTvurcuVysledku	4 (xsd:int)
http://linked.open...vavai/riv/projekt	Spectral theory of linear operators and reflexivity Methods of function theory and Banach algebras in operator theory IV Orbits, invariant subspaces and positivity in operator theory
http://linked.open...UplatneniVysledku	2013
http://linked.open...v/svazekPeriodika	264
http://linked.open...iv/tvurceVysledku	Müller, Vladimír Ambrozie, Calin-Grigore Bračič, J. Kuzma, B.
http://linked.open...ain/vavai/riv/wos	000314133700007
issn	0022-1236
number of pages	20 (xsd:int)
http://bibframe.org/vocab/doi	10.1016/j.jfa.2012.11.011

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