Moore-Penrose inverse of Gram operator on Hilbert C*-modules
| Autor: | Moslehian, M. S., Sharifi, K., Forough, M., Chakoshi, M. |
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| Rok vydání: | 2012 |
| Předmět: | |
| Zdroj: | Studia Math. 210 (2012), no.2, 189-196 |
| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: Improved and new results, 10 pages, to appear in Studia Math |
| Databáze: | arXiv |
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