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Journal of Analysis & Number Theory
An International Journal
               
 
 
 
 
 
 
 
 
 
 

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Volumes > Vol. 1 > No. 1

 
   

Multiplication Operators with Closed Range in Operator Algebras

PP: 1-5
Author(s)
P. Sam Johnson,
Abstract
Let B(H) denote the C ∗ -algebra of all bounded linear operators 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) = ST. Consider the following three statements: (i) T has closed range in H, (ii) LT has closed range in B(H), (iii) RT has closed range in B(H). It is proved that all these three statements are equivalent. Some possibilities of extending this result to Banach spaces have been discussed.

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