ACTA issues

## Strictly contractive compression on backward shift invariant subspaces over the torus

Keiji Izuchi, Rongwei Yang

Acta Sci. Math. (Szeged) 70:1-2(2004), 147-165
5805/2009

 Abstract. On the Hardy space over the torus \$H^2(\Gamma ^2)\$, the Toeplitz operators \$T_{z}\$ and \$T_{w}\$ are unilateral shifts of infinite multiplicity. Subspaces \$N\subset H^2(\Gamma ^2)\$ invariant under \$T^*_{z}\$ and \$T^*_{w}\$ are said to be backward shift invariant. This paper studies the compression of the pair \$(T_{z}, T_{w})\$ (denoted by \$(S_{z}, S_{w})\$) to \$N\$. Its focus lies on the case when \$S_z\$ is a strict contraction. Much information about \$N^{\perp }\$ can be deduced in this case. AMS Subject Classification (1991): 46E20, 47A20, 47A13 Received December 30, 2002, and in final form April 3, 2003. (Registered under 5805/2009.)