Abstract. The sub-direct sum, a generalization of normal sum operation for matrices was introduced by Fallat and Johnson [FaJo99]. Here, the definition of sub-direct sum is extended to operators between Hilbert spaces. Conditions for the sub-direct sum to have a nonnegative Moore--Penrose inverse are obtained when the summands themselves have nonnegative Moore--Penrose inverses. The converse problem is also considered.

DOI: 10.14232/actasm-013-307-8

AMS Subject Classification (1991): 47A05, 47H05, 15A09, 15A24

Keyword(s): sub-direct sum, Moore--Penrose inverse, group inverse, nonnegativity

Received September 2, 2013. (Registered under 57/2013.)