Vector norm inequalities for power series of operators in Hilbert spacesW.S. Cheung, S.S. Dragomir
In this paper, vector norm inequalities that provides upper bounds for the
Lipschitz quantity
|| f(T)x-f(V)x||
for power series
f(z) = ∑n=0∞
anzn,
bounded linear operators T, V on the Hilbert space H and
vectors x ϵ H are established. Applications in relation to
Hermite-Hadamard type inequalities and examples for elementary functions of
interest are given as well.
Tbilisi Mathematical Journal, Vol. 7(2) (2014), pp. 21-34 |