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RESEARCH PRODUCT
The Spectrum of Analytic Mappings of Bounded Type
Manuel MaestreLuiza A. MoraesDomingo GarcíaM.lilian Lourençosubject
Discrete mathematicsANÁLISE FUNCIONALhomomorphismApplied MathematicsSpectrum (functional analysis)Multiplicative functionBanach spaceholomorphic mappinganalytic structureBounded typeContinuous linear operatorBounded functionBanach algebraFréchet algebraBanach *-algebraAnalysisMathematicsdescription
Abstract A Banach space E is said to be (symmetrically) regular if every continuous (symmetric) linear mapping from E to E ′ is weakly compact. For a complex Banach space E and a complex Banach algebra F , let H b ( E , F ) denote the algebra of holomorphic mappings from E to F which are bounded on bounded sets. We endow H b ( E , F ) with the usual Frechet topology. M ( H b ( E , F ), F ) denotes the set of all non-null continuous homomorphisms from H b ( E , F ) to F . A subset of G EF on which the extension of Zalduendo is multiplicative is presented and it is shown that, in general, the sets G EF and M ( H b ( E , F ), F ) do not coincide. We prove that if E is symmetrically regular and every continuous linear mapping from E to F is weakly compact then there exists an analytic structure on M ( H b ( E , F ), F ).
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2000-05-01 | Journal of Mathematical Analysis and Applications |