On commutants and operator equations

dc.contributor.author	Khalagai, J.M.
dc.contributor.author	Kavila, M.
dc.date.accessioned	2013-05-07T10:32:47Z
dc.date.available	2013-05-07T10:32:47Z
dc.date.issued	2012
dc.identifier.citation	International Electronic Journal of Pure and Applied Mathematics Volume 5 No. 3 2012, 99-104	en
dc.identifier.uri	http://erepository.uonbi.ac.ke:8080/xmlui/handle/123456789/19755
dc.description.abstract	Let B(H) denote the algebra of bounded linear operators on a Hilbert Space H into itself. Given A,B ∈ B(H) define C(A,B) and R(A,B) : B(H) −→ B(H) by C(A,B)X = AX − XB and R(A,B)X = AXB − X. Our task in this note is to show that if A is one-one and B has dense range then C(A2,B2)X = 0 and C(A3,B3)X = 0 imply C(A,B)X = 0 for some X ∈ B(H). Similarly, if R(A2,B2)X = 0 and R(A3,B3)X = 0 then R(A,B)X = 0 for some X ∈ B(H).	en
dc.language.iso	en	en
dc.subject	commutant,	en
dc.subject	quasiaffinity	en
dc.subject	normal operator	en
dc.title	On commutants and operator equations	en
dc.type	Article	en
local.publisher	School of Mathematics University of Nairobi	en