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Multiplication Operators with Closed Range in Operator Algebras
by
P. Sam Johnson
National Institute of Technology, Mangalore, India
Coauthors: C. Ganesa Moorthy, Alagappa University, India
Let B(H) denote the C* algebra of all bounded linear transformations from a Hilbert space H into itself. Let T ∈ B(H). Define LT : B(H) → B(H) by LT (S) = T ±S and define RT : B(H) → B(H) by RT (S) = S ±T. Consider the following three statements :
(a) T has closed range in H.
(b) LT has closed range in B(H)
(c) RT has closed range in B(H).
It is proved by the authors that all these three statements are equivalent. Some possibilities of extending this result to Banach spaces have been discussed.
Date received: April 6, 2008
Copyright © 2008 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cawh-22.