Norm inequalities for a class of elementary operators generated by analytic functions with non-negative Taylor coefficients in ideals of compact operators related to p-modified unitarily invariant norms

摘要

Let Sigma(infinity)(n=1) (parallel to A(n)h parallel to(2) +parallel to A*(n)h parallel to(2) + parallel to B(n)h parallel to(2) + parallel to B*(n)h parallel to(2)) +infinity for all h in a Hilbert space H, for some families {A(n)}(n=1)(infinity) and {B-n}(n=1)(infinity) of bounded operators on H, where at least one of them consists of mutually commuting normal operators. If p = 2, Phi is a symmetrically normed (s.n.) function, Phi((P)) is its p-modification, Phi((P))* is a s.n. function adjoint to Phi((p)) and parallel to.parallel to(Phi(p)*) is a norm on the ideal rho(Phi(p)*)(H), associated to the s.n. function Phi((p))* then for all X is an element of rho(Phi(p)*)(H)