Partial isometries and pseudoinverses in semi-Hilbertian spaces

In this article the concepts of partial isometries, normal partial isometries and generalized projections in the context of operators defined on a semi-Hilbertian space are developed. In particular, we analyze the relationship between these operators and different notions of pseudoinverses in semi-Hilbertian spaces. Finally, we apply the results obtained to describe the set of weighted projections into closed subspaces.