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.)
|