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RESEARCH PRODUCT
Regularity and Algebras of Analytic Functions in Infinite Dimensions
Pablo GalindoManuel MaestreRichard M. AronDomingo Garcíasubject
Pure mathematicsApplied MathematicsGeneral MathematicsBounded functionStructure (category theory)Banach spaceBoundary (topology)HomomorphismSpace (mathematics)Continuous linear operatorMathematicsAnalytic functiondescription
A Banach space E E is known to be Arens regular if every continuous linear mapping from E E to E ′ E’ is weakly compact. Let U U be an open subset of E E , and let H b ( U ) H_b(U) denote the algebra of analytic functions on U U which are bounded on bounded subsets of U U lying at a positive distance from the boundary of U . U. We endow H b ( U ) H_b(U) with the usual Fréchet topology. M b ( U ) M_b(U) denotes the set of continuous homomorphisms ϕ : H b ( U ) → C \phi :H_b(U) \to \mathbb {C} . We study the relation between the Arens regularity of the space E E and the structure of M b ( U ) M_b(U) .
| year | journal | country | edition | language |
|---|---|---|---|---|
| 1996-01-01 | Transactions of the American Mathematical Society |