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Let f (z) := P 1 n=0 anz n be a power series with complex coe¢cients and convergent on the open disk D (0; R) ; R > 0: If T; V 2 B (H) are such that kT k ; kV k < R; then we show among others that : Applications in connection with the Hermite-Hadamard inequality for Lipschitzian functions are provided as well. 1991 Mathematics Subject Classi...cation. 47A63; 47A99.doi:10.3836/tjm/1391177983 fatcat:2dhztrtyvfhbrizcz2hvawwwjy