The reverse order law for Moore-Penrose inverses of operators on Hilbert\n C*-modules

2014/03/25 by Kamran Sharifi, Sharifi, Kamran, Behnaz Ahmadi Bonakdar +1
Mathematics · Computer Science · #Spectral Theory in Mathematical Physics #Matrix Theory and Algorithms #Mathematical Analysis and Transform Methods

paper · pdf · doi:10.48550/arxiv.1403.6510

Abstract

Suppose T and S are bounded adjointable operators between Hilbert\nC*-modules admitting bounded Moore-Penrose inverse operators. Some necessary\nand sufficient conditions are given for the reverse order law (TS) ^dag\n=S ^dag T ^dag to hold. In particular, we show that the equality holds\nif and only if Ran(T^\∗TS) \⊆ Ran(S) and Ran(SS^\∗T^\∗)\n\⊆ Ran(T^\∗), which was studied first by Greville [ it SIAM Rev. 8\n(1966) 518--521] for matrices.\n

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