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

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  • Ruifang Zhao

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.

Suggested Citation

  • Ruifang Zhao, 2012. "A Similarity Invariant and the Commutant of some Multiplication Operators on the Sobolev Disk Algebra," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2012, pages 1-17, September.
    • Handle: RePEc:hin:jijmms:378217
    DOI: 10.1155/2012/378217
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