SOME OPERATOR ORDER INEQUALITIES FOR CONTINUOUS FUNCTIONS OF SELFADJOINT OPERATORS IN HILBERT SPACES

Various bounds in the operator order for the following operator transform ~ f (A) := 1 (f (A) f ((m + M)1H A)); where A is a selfadjoint operator in the Hilbert space H with the spectrum Sp(A) � (m;M) and f : (m;M) ! C is a continuous function on (m;M) are given. Applications for the power and logaritmic functions are provided as well.