. "264" . . . "20"^^ . "66045" . "The commuting graph of bounded linear operators on a Hilbert space"@en . . . "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." . . . "I, P(GA201/09/0473), P(IAA100190903), P(MEB091101)" . . . "0022-1236" . . . "RIV/67985840:_____/13:00386898!RIV13-AV0-67985840" . "M\u00FCller, Vladim\u00EDr" . "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 . "Journal of Functional Analysis" . "The commuting graph of bounded linear operators on a Hilbert space"@en . "The commuting graph of bounded linear operators on a Hilbert space" . "000314133700007" . . "Ambrozie, Calin-Grigore" . . "US - Spojen\u00E9 st\u00E1ty americk\u00E9" . "Hilbert space; operators; commutativity"@en . "[8BC2F54CD819]" . "4" . "The commuting graph of bounded linear operators on a Hilbert space" . "10.1016/j.jfa.2012.11.011" . "RIV/67985840:_____/13:00386898" . . . . . . "2"^^ . "Bra\u010Di\u010D, J." . . . "4"^^ . "Kuzma, B." .