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Bull. Korean Math. Soc. 2006; 43(4): 671-677
Printed December 1, 2006
Copyright © The Korean Mathematical Society.
On the range closure of an elementary operator
J. A. Canavati, S. V. Djordjevi'c, and B. P. Duggal
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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