Subspace gaps and Weyl's theorem for an elementary operator

B. P. Duggal

International Journal of Mathematics and Mathematical Sciences, 2005, vol. 2005, 1-10

Abstract:

A range-kernal orthogonality property is established for the elementary operators ℰ ( X ) = ∑ i = 1 n A i X B i and ℰ * ( X ) = ∑ i = 1 n A i * X B i * , where A = ( A 1 , A 2 , … , A n ) and B = ( B 1 , B 2 , … , B n ) are n -tuples of mutually commuting scalar operators (in the sense of Dunford) in the algebra B ( H ) of operators on a Hilbert space H . It is proved that the operator ℰ satisfies Weyl's theorem in the case in which A and B are n -tuples of mutually commuting generalized scalar operators.

Date: 2005
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:389358

DOI: 10.1155/IJMMS.2005.465

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