On a revisited Moore-Penrose inverse of a linear operator on Hilbert spaces

[EN] For two given Hilbert spaces H and K and a given bounded linear operator A is an element of L(H, K) having closed range, it is well known that the Moore-Penrose inverse of A is a reflexive g-inverse G is an element of L ( K; H) of A which is both minimum norm and least squares. In this paper, weaker equivalent conditions for an operator G to be the Moore-Penrose inverse of A are investigated in terms of normal, EP, bi-normal, bi-EP, l-quasi-normal and r-quasi-normal and l-quasi-EP and r-quasi-EP operators.Research partially supported by Ministerio de Economia y Competitividad of Spain (grant DGI MTM2013-43678-P and Red de Excelencia MTM2015-68805-REDT)Malik, SB.; Thome, N. (2017). On a revisited Moore-Penrose inverse of a linear operator on Hilbert spaces. Filomat. 31(7):1927-1931. https://doi.org/10.2298/FIL1707927M1927193131