A product integral representation of the generalized inverse
Charles W. Groetsch · Czech digital mathematics library · 1975
Suppose A s«£(Hn,H^) has closed range where H-^ and H 2 are Hilbert spaces.Let S c CO, co ) be such that Oe S and sup-It: t € S} = co and suppose g: : S->CO,oo ) is an increasing function with g(O) = 0 and g(t)-*co as t-*co .Let WCt) = ft* r I -dg tl where t is the restriction of A* A to H = R( A*) and suppose W(t)-> 0 uniformly in & (H,H) as t^oo .If M(t) = = (L) ff W( • )A* dg then A* = lim M(t) uniformly in it (Hp,Hn) .This generalizes some well known representations of A + .