A Similarity Invariant and the Commutant of some Multiplication Operators on the Sobolev Disk Algebra.

Let R(픻) be the algebra generated in Sobolev space W²²(픻) by the rational functions with poles outside the unit disk ̅픻. In this paper, we study the similarity invariant of the multiplication operators M_g in L(R(픻)), when g is univalent analytic on 픻 or M_g is strongly irreducible. And the commutants of multiplication operators whose symbols are composite functions, univalent analytic functions, or entire functions are studied. [ABSTRACT FROM AUTHOR]