Moore-Penrose inverse of Gram operator on Hilbert C*-modules

Abstract

Let $t$ be a regular operator between Hilbert $C^{\ast }$-modules and $t^{†}$ be its Moore-Penrose inverse. We investigate the Moore-Penrose invertibility of the Gram operator $t^{\ast }t$. More precisely, we study some conditions ensuring that $t^{†}=(t^{\ast }t{)}^{†}{t}^{\ast }=t^{\ast }(t{t}^{\ast }{)}^{†}$ and $(t^{\ast }t{)}^{†}=t^{†}{t}^{\ast †}$ hold. As an application, we get some results for densely defined closed operators on Hilbert $C^{\ast }$-modules over $C^{\ast }$-algebras of compact operators.

Improved and new results, 10 pages, to appear in Studia Math

References in corpus (1)

• The gap between unbounded regular operators