An invariance property of operator products related to the mixed-type reverse order laws. Issue 5 (3rd May 2016)

• Record Type: Journal Article
• Authors: Liu, Xiaoji; Fu, Shiqin; Yu, Yaoming
• Is Part Of: Linear & multilinear algebra. Volume 64:Issue 5(2016)
• Page Start: 885
• Page End: 896
• Publication Date: 2016-05-03
• Subjects: generalized inverse -- invariance property -- mixed-type reverse order law -- operator product; 47A05 -- 15A09; Algebras, Linear -- Periodicals; Multilinear algebra -- Periodicals; 512.505
• DOI: 10.1080/03081087.2015.1065786
• Languages: English
• ISSNs: 0308-1087

Abstract

Abstract : In this paper, we derive an interesting result that the mixed-type reverse order laws hold if and only if the bounded linear operator products is invariant, where is taken, for instance, as, , , , as well as . Moreover, the invariance property of is related to the reverse order law, and we point out that such an invariance property occurs if and only if and are left or and are right invertible operators, or is left and is right invertible operator, where, and are nonzero regular operators.