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The Dunford‐Pettis Property for some Function Algebras in Several Complex Variables
Author(s) -
Li SongYing,
Russo Bernard
Publication year - 1994
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/50.2.392
Subject(s) - polydisc , bounded function , mathematics , unit sphere , bergman kernel , pure mathematics , boundary (topology) , bergman space , property (philosophy) , unit (ring theory) , type (biology) , algebra over a field , holomorphic function , discrete mathematics , mathematical analysis , ecology , mathematics education , biology , philosophy , epistemology
The Dunford‐Pettis property is shown to hold for the uniform algebra A (Ω) and its dual for some standard domains Ω, including strongly pseudoconvex bounded domains in C n , pseudoconvex bounded domains of finite type in C 2 , and bounded domains in C. Previously the result was known for the unit ball and unit polydisc in C n . Techniques used involve Bourgain algebras, Hankel operators, properties of the Bergman kernel, quasi‐metrics on the boundary, and ∂̅‐theory.
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