MODULUS OF QUASIDIAGONALITY by S.C.Arora and Anuradha, Delhi, India

Abstract. If qd(T) denotes the modulus of quasidiagonality of an operator T on a Hilbert space, it is proved that the mapping T → qd(T) is uniformly continuous and T is quasidiagonal if and only if qd(T) = 0. For any invertible operator S, an upper bound for qd(S^{−1}T S) is obtained. It is also proved if M is an invariant subspace of T, then

qd(T) ≤ max{qd(T |_{M}), qd(T |_{M^{⊥}})}.

Mathematics subject classification: 47A66, 47A30 Keywords: Quasitriangular, quasidiagonal operators, modulus of quasitriangularity, modulus of quasidiagonality, orthogonal projections, strong convergence.