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

M. S. Moslehian; K. Sharifi; M. Forough; M. Chakoshi

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

Functional Analysis 2013-04-02 v2 Operator Algebras

Authors: M. S. Moslehian , K. Sharifi , M. Forough , M. Chakoshi

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.

Keywords

moore-penrose inverse gram operator hilbert c*-modules regular operator c*-algebras closed operators

Cite

@article{arxiv.1205.3852,
  title  = {Moore-Penrose inverse of Gram operator on Hilbert C*-modules},
  author = {M. S. Moslehian and K. Sharifi and M. Forough and M. Chakoshi},
  journal= {arXiv preprint arXiv:1205.3852},
  year   = {2013}
}

Comments

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

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

Abstract

Keywords

Cite

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