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 (SS
−1 − 1)SXS
−1 + S
−1XS
I .