The Dunford-Pettis Property for some Function Algebras in Several Complex Variables |
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| Authors: | Li Song-Ying; Russo Bernard |
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| Institution: | Department of Mathematics, University of California Irvine, California 92717, USA E-mail: BRUSSO{at}MATH.UCI.EDU, SLI{at}MATH.UCI.EDU |
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| Abstract: | The Dunford-Pettis property is shown to hold for the uniformalgebra A( ) and its dual for some standard domains , includingstrongly pseudoconvex bounded domains in Cn, pseudoconvex boundeddomains of finite type in C2, and bounded domains in C. Previouslythe result was known for the unit ball and unit polydisc inCn. Techniques used involve Bourgain algebras, Hankel operators,properties of the Bergman kernel, quasi-metrics on the boundary,and  -theory. |
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