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arXiv · 1205.3852

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

M. S. Moslehian·K. Sharifi·M. Forough·M. Chakoshi
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Abstract

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

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M. S. Moslehian, K. Sharifi, M. Forough, M. Chakoshi. 2012-05-17. Moore-Penrose inverse of Gram operator on Hilbert C*-modules. https://arxiv.org/abs/1205.3852

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