A Spectral Representation for Weakly Periodic Sequences F Bounded Linear Transformations

A spectral representation for certain sequences of bounded linear transformations between two Hilbert spaces, namely; weakly periodic, is given. In this representation the elements of a weakly periodic sequence, {An, n Z} L(X, Y), are viewed, in the weak sense, as the Fourier coefficients of a certain set function on the Borel sets of 0, 2) with values in L(X, Y).