ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

8. Analysis

1991 MS Classification: 47 Abkar, Ali, Lund University, Sweden A comparison theorem concerning hyperinvariant subspaces on finitely connected domains Let Ω be a finitely connected domain, and X a (quasi) Banach space of analytic functions on Ω. We prove a theorem which converts the study of hyperinvariant subspaces of X into the study of those of X_{1} where X_{1} is some similar space on Ω_{1}, a simply connected domain obtained from Ω by adding some of the bounded components of ℂ \ Ω. Let M(X) denote the multiplier space consisting of those f for which f · X ⊂ X. Then (under some reasonable conditions) I ↦ clos(I · M(X)) supplies a one-to-one correspondence between a class of hyperinvariant subspaces of X_{1} and a class of hyperinvariant subspaces of X. Furthermore the inverse mapping is given by J ↦ J ∩ X_{1}. This result is joint work with H. Hedenmalm.