  A certain class of matrix-valued Borel matrix functions is introduced and it
is shown that all functions of that class naturally operate on any operator T
in a finite type I von Neumann algebra M in a way such that uniformly bounded
sequences f_1,f_2,... of functions that converge pointwise to 0 transform into
sequences f_1[T],f_2[T],... of operators in M that converge to 0 in the
*-strong operator topology. It is also demonstrated that the double *-commutant
of any such operator T which acts on a separable Hilbert space coincides with
the set of all operators of the form f[T] where f runs over all function from
the aforementioned class. Some conclusions concerning so-called
operator-spectra of such operators are drawn and a new variation of the
spectral theorem for them is formulated.
