Toeplitz operators associated with analytic crossed products. II: Invariant subspaces and factorization (Q1175035)

The author considers Toeplitz operators \(T_ A\) acting on a space \({\mathcal H}^ 2=\ell^ 2(Z_ +,L^ 2(M))\), where \(L^ 2(M)\) consists of vector-valued functions determined by a von Neumann algebra \(M\) and a \(^*\)-isomorphism \(\alpha\), and where the symbol \(A\) is generated by analogues of the shift operators. The author obtains results concerning the structure of invariant subspaces for \(T_ A\), factorizations, and the Szegö infimum problem that generalizes known results in the classical case of the unit circle. [For part I see Math. Proc. Camb. Philos. Soc. 108, No. 3, 539-549 (1990; Zbl 0731.47026)].