Quasi-Diagonal Operators
DOI:
https://doi.org/10.5644/SJM.06.2.07Keywords:
Quasi-diagonal operatorsAbstract
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 $TT^*\in (QD)(P_n)$ if and only if $T^*T\in (QD)(P_n).$ 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 $P_n\rightarrow I$ strongly, then $T=N+K,$ where $N$ is a normal operator and $K$ is a compact operator.
2000 Mathematics Subject Classification. 47Bxx, 47B20
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References
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