Invariant subspaces on multiply connected domains.

Título inglés	Invariant subspaces on multiply connected domains.
Título español	Subespacios invariantes en dominios múltiplemente conexos.
Autor/es	Abkar, Ali ; Hedenmalm, Hakan
Organización	Dep. Math. Lund Univ., Lund, Suecia
Revista	0214-1493
Publicación	1998, 42 (2): 521-557, 36 Ref.
Tipo de documento	articulo
Idioma	Inglés
Resumen inglés	The lattice of invariant subspaces of several Banach spaces of analytic functions on the unit disk, for example the Bergman spaces and the Dirichlet spaces, have been studied recently. A natural question is to what extent these investigations carry over to analogously defined spaces on an annulus. We consider this question in the context of general Banach spaces of analytic functions on finitely connected domains Ω­. The main result reads as follows: Assume that B is a Banach space of analytic functions satisfying some conditions on the domain Ω­. Assume further that M(B) is the set of all multipliers of B. Let ­Ω1 be a domain obtained from ­Ω by adding some of the bounded connectivity components of CΩ­. Also, let B1 be the closed subspace of B of all functions that extend analytically to Ω1. Then the mapping I → clos(I · M(B)) gives a one-to-one correspondence between a class of multiplier invariant subspaces I of B1, and a class of multiplier invariant subspaces J of B. The inverse mapping is given by J → J ∩ B1.
Clasificación UNESCO	120203
Palabras clave español	Subespacio invariante ; Espacios de Banach ; Funciones analíticas ; Multiplicadores ; Retículos ; Operadores lineales
Código MathReviews	MR1676042
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