Weak crossed products and a generalisation of a result of Sarason Original Research Article

In this paper, the weak semicrossed products of finite dimensional W*-algebras by Z+ are identified with algebras of matrices of functions of H∞(T) and then they are classified up to algebraic isomorphism. In the second part of the paper, the weak operator density of matrices of polynomials in the unit ball of our main algebra is shown. Moreover, a generalisation of a result due to D. Sarason [Trans. Amer. Math. Soc. 127 (1967) 179–203] about the closure of H∞(T)+C(T) in L∞(T) is obtained.