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Algebras of holomorphic mappings in (DF)-spaces
Authors:AL Aguiar  LA Moraes
Institution:a C.P. 1010, CEP 57022-970, Maceió, AL, Brazil
b Instituto de Matemática, Universidade Federal do Rio de Janeiro, CP 68530, CEP 21945-970 Rio de Janeiro, RJ, Brazil
Abstract:Let U be an absolutely convex open subset of a complex barrelled (DF)-space E and let F be a commutative Banach algebra with identity. Let Hb(U, F) be the space of holomorphic mappings from U into F that are bounded on the U-bounded sets and let Hb (U, F) be the space of the holomorphic mappings from U into F that are uniformly weakly continuous on the U-bounded sets, both endowed with the topology τb of uniform convergence on the U-bounded sets. The spectra of (Hwu (U, F), τb) and (Hb(U, F), τb) are studied.
Keywords:46G25  46G20
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