arXiv subjects

M. Chakoshi

Publications and source records attributed to M. Chakoshi.

2 recordsLinked to original sources

arXiv2012

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

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

math.FA↗

arXiv2012

Quasi-representations of Finsler modules over C*-algebras

We show that every Finsler module over a $C^*$-algebra has a quasi-representation into the Banach space $\mathbb{B}(\mathscr{H},\mathscr{K})$ of all bounded linear operators between some Hilbert spaces $\mathscr{H}$ and $\mathscr{K}$. We define the notion of completely positive $φ$-morphism and establish a Stinespring type theorem in the framework of Finsler modules over $C^*$-algebras. We also investigate the nondegeneracy and the irreducibility of quasi-representations.

math.OA↗