NUMERICAL RADIUS AND p-SCHATTEN NORM INEQUALITIES FOR POWER SERIES OF OPERATORS IN HILBERT SPACES.

Let H be a complex Hilbert space. Assume that the power series with complex coefficients f (z) := ∑^∞_k=0 a_kz^k is convergent on the open disk D(0, R), f_a (z) := ∑^∞k=0 |a_k| z^k that has the same radius of convergence R and A, B, C ∊ B (H) with ||A|| < R, then we have the following Schwarz type inequality ... for α ∊ [0, 1] and x, y ∊ H. Some natural applications for numerical radius and p-Schatten norm are also provided. [ABSTRACT FROM AUTHOR]