On two-sidedH∗-algebras
Parfeny P. Saworotnow · Pacific Journal of Mathematics · 1966
We call a Banach algebraA, whose norm is a Hubert space norm, a two-sided H*-algebra if for each x e A there are elements x ι 9 x r in A such that (xy, z) = (y, x ι z) and (yx, z) -(y, zx r ) for all y, z e A. A two-sided iί *-algebra is called discrete is each right ideal R such that {x r \xeR} = {x ι \xeR} contains an idempotent e such that e r = e ι = e.The purpose of this paper is to obtain a structural characterization of those two-sided H *-algebras M which consist of complex matrices x = (Xij \i, je J) (J is any index set) for which Σ UIxu \% converges.Here U is real and 1 ^ U ^ a for all i e J and some real a.The inner product in M is (»j l/) = Σ tiXisyats id and «iy = (tiltj)Xji , X\j = (tjlU)Xji .