© Hindawi Publishing Corp. SOME INEQUALITIES IN B(H)

Abstract. Let H denote a separable Hilbert space and let B(H) be the space of bounded and linear operators from H to H. We define a subspace ∆(A,B) of B(H), and prove two inequalities between the distance to ∆(A,B) of each operator T in B(H), and the value sup{‖AnTBn−T ‖:n = 1,2,...}