Title of article :
Jensen s Operator and Applications to Mean Inequalities for Operators in Hilbert Space
Author/Authors :
Krnic, Mario University of Zagreb - Faculty of Electrical Engineering and Computing, Croatia , Lovricevic, Neda University of Split - Faculty of Civil Engineering and Architecture, Croatia , Pecaric, Josip University of Zagreb - Faculty of Textile Technology, Croatia
Abstract :
In this paper we consider Jensen s operator, which includes bounded self-adjoint operator on Hilbert space, and investigate its properties. Due to derived properties, we find lower and upper bound for Jensen s operator, which are multiples of non-weighted Jensen s operator. On the other hand, we also establish some bounds for spectra of Jensen s operator by means of discrete Jensen s functional. The obtained results are then applied to operator means. In such a way, we get refinements and conversions of numerous mean inequalities for Hilbert space operators.
Keywords :
Jensen s inequality , Jensen s functional , Jensen s oper , ator , Hilbert space , bounded self , adjoint operator , positive invertible operator , arithmetic operator mean , geometric operator mean , harmonic operator mean , superadditivity , monotonicity , renement , conversion , Kantorovich constant.
Journal title :
Bulletin of the Malaysian Mathematical Sciences Society
Journal title :
Bulletin of the Malaysian Mathematical Sciences Society
