The commuting graph of bounded linear operators on a Hilbert space

0386898 - MÚ 2013 RIV US eng J - Journal Article
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
R&D Projects: GA ČR GA201/09/0473; GA AV ČR IAA100190903; GA MŠMT(CZ) MEB091101
Institutional support: RVO:67985840
Keywords : Hilbert space * operators * commutativity
Subject RIV: BA - General Mathematics
Impact factor: 1.152, year: 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.
Permanent Link: http://hdl.handle.net/11104/0218604