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

Abstract EN

Let R(?) be the algebra generated in Sobolev space W22(?) by the rational functions with poles outside the unit disk ?¯.

In this paper, we study the similarity invariant of the multiplication operators Mg in ℒ(R(?)), when g is univalent analytic on ? or Mg is strongly irreducible.

And the commutants of multiplication operators whose symbols are composite functions, univalent analytic functions, or entire functions are studied.