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# Wydawnictwa / Czasopisma IMPAN / Studia Mathematica / Wszystkie zeszyty

## Moore–Penrose inverses of Gram operators on Hilbert $C^*$-modules

### Tom 210 / 2012

Studia Mathematica 210 (2012), 189-196 MSC: Primary 46L08; Secondary 47A05, 15A09, 46L05. DOI: 10.4064/sm210-2-6

#### Streszczenie

Let $t$ be a regular operator between Hilbert $C^*$-modules and $t^\dagger$ 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 $t^{ \dagger} = (t^* t)^{ \dagger} t^*= t^*(t t^*)^{ \dagger}$ and $(t^*t)^{\dagger}=t^{ \dagger}t^{* \dagger}$. As an application, we get some results for densely defined closed operators on Hilbert $C^*$-modules over $C^*$-algebras of compact operators.

#### Autorzy

• M. S. MoslehianDepartment of Pure Mathematics
Center of Excellence in Analysis
on Algebraic Structures (CEAAS)
P.O. Box 1159, Mashhad 91775, Iran
e-mail
• K. SharifDepartment of Mathematics
Shahrood University of Technology
P.O. Box 3619995161-316, Shahrood, Iran
and
School of Mathematics
Institute for Research
in Fundamental Sciences (IPM)
P.O. Box 19395-5746, Tehran, Iran
e-mail
• M. ForoughDepartment of Mathematics