the basic fact about infinite products of complex numbers is that is convergent if and only if converges. does anyone know if something of this kind holds for matrix-valued case?
I hope for converges if .
an easier related statement, which looks very true (but I still don't know solution yet) is to prove converges if (here 's are not assumed to commute, of course)
if anyone saw this matter addressed in any book or science paper, I'd appreciate the reference