Quasi-Diagonal Operators - Lohaj, Muhib; Lohaj, Shqipe (Sarajevo Journal of Mathematics, 2024)
Let H be a separable complex Hilbert space and let B(H) denote the algebra of all bounded linear operators on H. If T is a quasi-normal Fredholm operator we prove that TT^*(QD)(P_n) if and only if T^*T(QD)(P_n). We also show that if T is quasi-normal and T(T^*T) is quasi-diagonal with respect to any sequence (P_n) in PF(H), such that P_n→ I strongly, then T=N+K, where N is a normal operator and K is a compact operator. 2000 Mathematics Subject Classification. 47Bxx, 47B20