On the range closure of an elementary operator
Bull. Korean Math. Soc. 2006 Vol. 43, No. 4, 671-677
Published online December 1, 2006
J. A. Canavati, S. V. Djordjevi'c, and B. P. Duggal
Abstract : Let $A, B\in B(H)$ be Hilbert space contractions, and let $\t$ be the elementary operator $\t:X\longrightarrow AXB-X$. A number of conditions which are equivalent to `` $\triangle_{AB}$ has closed range" are proved.
Keywords : elementary operators, quasinilpotent part, numerical range, pole, orthogonality
MSC numbers : 47B47, 47A10, 47A11
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