The commuting graph of bounded linear operators on a Hilbert space

0386898 - MÚ 2013 RIV US eng J - Článek v odborném periodiku
Ambrozie, Calin-Grigore - Bračič, J. - Kuzma, B. - Müller, Vladimír
The commuting graph of bounded linear operators on a Hilbert space.
Journal of Functional Analysis. Roč. 264, č. 4 (2013), s. 1068-1087. ISSN 0022-1236. E-ISSN 1096-0783
Grant CEP: GA ČR GA201/09/0473; GA AV ČR IAA100190903; GA MŠMT(CZ) MEB091101
Institucionální podpora: RVO:67985840
Klíčová slova: Hilbert space * operators * commutativity
Kód oboru RIV: BA - Obecná matematika
Impakt faktor: 1.152, rok: 2013
http://www.sciencedirect.com/science/article/pii/S002212361200420X#

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.
Trvalý link: http://hdl.handle.net/11104/0218604