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

Abstract

For a probability measure µ on Ω and square integrable (Hilbert space) operator valued functions (formula presented), we prove Grüss-Landau type operator inequality for inner product type transformers (formula presented) for all X ∈ B(H) and for all η ∈ [0, 1]. Let p ≥ 2, Φ to be a symmetrically norming (s.n.) function, Φ^(p) to be its p-modification, Φ^(p) ^∗ is a s.n. function adjoint to Φ^(p) and (formula presented) to be a norm on its associated ideal C<inf>Φ</inf> (p) ∗ (H) of compact operators. If (formula presented) is a sequence in (0, 1], such that(formula presented) for some families {A<inf>n</inf> }^{∞ and {B}n=1 n}^∞of bounded operators on Hilbert space H and for all f ∈ H, then (formula presented) if at least one of those operator families consists of mutually commuting normal operators. The related Grüss-Landau type (formula presented) norm inequalities for inner product type transformers are also provided.