01794nab a2200229 i 4500 publ37372 20250804145342.0 250804s2021 hu o 000 eng d 0378-620X 10.1007/s00020-020-02605-5 doi 31862557 mtmt SZTE Publicatio Repozitórium hun eng Molnár Lajos On Functional Representations of Positive Hilbert Space Operators [elektronikus dokumentum] / Molnár Lajos 2021 28 INTEGRAL EQUATIONS AND OPERATOR THEORY 93 No. 1 In this paper we consider some faithful representations of positive Hilbert space operators on structures of nonnegative real functions defined on the unit sphere of the Hilbert space in question. Those representations turn order relations between positive operators to order relations between real functions. Two of them turn the usual Löwner order between operators to the pointwise order between functions, another two turn the spectral order between operators to the same, pointwise order between functions. We investigate which algebraic operations those representations preserve, hence which kind of algebraic structure the representing functions have. We study the differences among the different representing functions of the same positive operator. Finally, we introduce a new complete metric (which corresponds naturally to two of those representations) on the set of all invertible positive operators and formulate a conjecture concerning the corresponding isometry group. Matematika Ramanantoanina Andriamanankasina aut http://publicatio.bibl.u-szeged.hu/37372/1/OnFunctionalRepresentationsofPositiveHilbertSpaceOperators.pdf Dokumentum-elérés