hi,

here is the standard definition of L_2-space of matrix-valued functions: it's those measurable F that satisfy

(i)

(or equivalently, , or )

(here is the adjoint of )

clearly this implies

(ii)

what about the converse -- does (ii) necessarily implies (i), i.e. is (ii) enough for the function to be in L_2?

for the scalar case (i)=(ii), but I suspect (and afraid) that this fails for matrices...

...help...