Milena Venkova

Holomorphically dependent generalised inverses

In this article we investigate when the pointwise existence of a generalised inverse for holomorphic operator-valued mappings defined on domains in a Banach space implies the existence of a holomorphic generalised inverse.ResumenEn este artículo investigamos cuándo la existencia puntual de una inversa generalizada de una aplicación holomorfa operador-valuada definida en un dominio de un espacio de Banach implica la existencia de una inversa generalizada holomorfa.

Fredholm-valued holomorphic mappings on a Banach space

Abstract In this article we show that the pointwise existence of a regulariser for holomorphic Fredhom-valued mappings defined on pseudo-convex domains in Banach spaces with an unconditional basis implies the existence of a holomorphic regulariser.

HOLOMORPHIC NEAR INVERSES

In this article we show that holomorphic Fredholm-valued mappings defined on connected pseudo-convex domains in Banach spaces with unconditional basis always have meromorphic generalised inverses. We show they have holomorphic generalised inverses if and only if the kernels have the same dimension at all points in Ω.

Injective tensor products of tree spaces

We study tensor products on tree spaces; in particular, we give necessary and sufficient conditions for the n-fold injective tensor product of tree spaces to contain a copy of `1.