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INICIO | 27 de julio de 2024
  

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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Equipo DML-E
Instituto de Ciencias Matemáticas (ICMAT - CSIC)
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