We characterize the class of continuous bilinear mappings F from C1[0,1]×C1[0,1] to a Banach space X with the property that fg=0 implies F(f,g)=0. This result is used in the study of zero-product preservers on C1[0,1] and in the study of operators on C1[0,1] that enjoy a certain localisation property.
COBISS.SI-ID: 14892377
We construct proper holomorpic embeddings in nC2 of those bordered Riemann surfaces that admit an injective holomorphic map into C2.
COBISS.SI-ID: 15395417
It is proved that the basic Oka property of a complex manifold also implies the parametric Oka property. This result unifies the existing theory of Oka properties, and we introduce this class as Oka manifolds. Corollary: If E is a holomorphic fiber bundle with an Oka fiber over B, then E is an Oka manifold if and only if B is an Oka manifold.
COBISS.SI-ID: 15395161
Let U be the open unit disc in C, p a point in the unit circle, and f a continuous function on the closure of U that extends holomorphically from every circle centered at the origin and also from every circle in the closure of U that contains the point p. Then f is holomorphci on U.
COBISS.SI-ID: 15392601
In the paper the author constructs proper holomorphic embeddings of certain infinitely connected bordered Riemann surfaces into C2.
COBISS.SI-ID: 15118681