We study the invariant subspaces of the operator M_z on the Sobolev disk algebra R(D).First,we study the multiplication operator M_z restricted to the invariant subspace.Then we show that M_z restricted to one invariant subspace is unitarily equivalent to M_z restricted to another invariant subspace if and only if the two invariant subspaces are equal.We also characterize the invariant subspaces with common zeros on the boundary of the disk.
Rui Fang ZHAO; Yong-fei Jin.
The Invariant Subspaces of the Sobolev Disk Algebra. Acta Mathematica Sinica, Chinese Series, 2008, 51(3): 617-624 https://doi.org/10.12386/A2008sxxb0073