Abstract

Let B(H) be the C ∗ -algebra of all bounded linear operators on a complex Hilbert space H, S be an invertible and selfadjoint operator in B(H) and let ( I,∥.∥ I ) denote a norm ideal of B(H). In this note, we shall show the following inequality: ∀X∈I:∥SXS −1−S −1XS∥ I⩽(∥S∥∥S −1∥−1)∥SXS −1+S −1XS∥ I.

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