# Weighted Moore–Penrose inverses of products and differences of weighted projections on indefinite inner-product spaces

Weighted Moore–Penrose inverses of products and differences of weighted projections on indefinite... An adjointable operator acting on a Hilbert C∗\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$C^*$$\end{document}-module is called a weight if it is self-adjoint and invertible. An indefinite inner-product space as well as weighted projections can be induced by a weight. Some new formulas are provided for weighted Moore–Penrose inverses associated to products and differences of weighted projections. As a result, some characterizations of Moore–Penrose inverses associated to projections are generalized to the weighted case. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Advances in Operator Theory Springer Journals

# Weighted Moore–Penrose inverses of products and differences of weighted projections on indefinite inner-product spaces

, Volume 5 (3) – Jul 19, 2020
20 pages

/lp/springer-journals/weighted-moore-penrose-inverses-of-products-and-differences-of-kOrar0aHc2
Publisher
Springer Journals
ISSN
2662-2009
eISSN
2538-225X
DOI
10.1007/s43036-020-00057-7
Publisher site
See Article on Publisher Site

### Abstract

An adjointable operator acting on a Hilbert C∗\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$C^*$$\end{document}-module is called a weight if it is self-adjoint and invertible. An indefinite inner-product space as well as weighted projections can be induced by a weight. Some new formulas are provided for weighted Moore–Penrose inverses associated to products and differences of weighted projections. As a result, some characterizations of Moore–Penrose inverses associated to projections are generalized to the weighted case.