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

Ruifang Zhao

International Journal of Mathematics and Mathematical Sciences, 2012, vol. 2012, 1-17

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.

Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:378217

DOI: 10.1155/2012/378217

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