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

Grüss-Landau inequalities for elementary operators and inner product type transformers in Q and Q* norm ideals of compact operators

“…family. The terminology used in this paper is closely related to the that one used in [10], and a more detailed introduction therein may contribute to the comfort of the reader of this article itself. For a more complete account on the theory of norm ideals, the reader is referred to [1,3,14].…”

“…As(10) is just a special case X • • = I in (5) of Theorem 2.1, the final inequalities in(11) follows by the monotonicity of operator norm on positive operators and operator monotonicity of function t → t η on [0, ∞). The commutativity requirement that ϕ and Φ (resp.…”