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Compact and Weakly Compact Homomorphisms on Fréchet Algebras of Holomorphic Functions
Author(s) -
Galindo Pablo,
Lourenço Lilian,
Moraes Luiza A.
Publication year - 2002
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/1522-2616(200203)236:1<109::aid-mana109>3.0.co;2-y
Subject(s) - mathematics , bounded function , homomorphism , approximation property , holomorphic function , pure mathematics , algebra homomorphism , banach space , pointwise , rank (graph theory) , discrete mathematics , combinatorics , mathematical analysis
We study homomorphisms between Fréchet algebras of holomorphic functions of bounded type. In this setting we prove that any pointwise bounded homomorphism into the space of entire functions of bounded type is rank one. We characterize up to the approximation property of the underlying Banach space, the weakly compact composition operators on H b ( V ), V absolutely convex open set.