A Similarity Invariant and the Commutant of some Multiplication Operators on the Sobolev Disk Algebra. (2nd September 2012) - Zhao, Ruifang
Abstract : Let R ( 𝔻 ) be the algebra generated in Sobolev space W 22 ( 𝔻 ) by the rational functions with poles outside the unit disk 𝔻 ¯ . In this paper, we study the similarity invariant of the multiplication operators M g in ℒ ( R ( 𝔻 ) ), when g is univalent analytic on 𝔻 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.