Further characterizations of $k$-generalized projectors and $k$-hypergeneralized projectors]{Further characterizations of $k$-generalized projectors and $k$-hypergeneralized projectors

Abstract

The paper focuses on the classes of the $k$-generalized and $k$-hypergeneralized projectors. Several original features of these classes are identified and new properties characterized. We present some relations between $k$-generalized and $k$-hypergeneralized projectors that generalize appropriate relations between generalized and hypergeneralized projectors given in [Further properties of generalized and hypergeneralized projectors, Linear Algebra and its Applications, 389 (2004) 295--303] and [Further results on generalized and hypergeneralized projectors, Linear Algebra and its Applications, 429 (2008) 1038--1050].