RMC - Vol. 6, Num. 2 - Christopher Boyd

Full paper in PDF:
$%C. Boyd, Distinguished preduals of spaces of holomorphic functions, Rev. Mat. Univ. Complut. Madrid 6 (1993), no. 2, 221–231.%$

Distinguished Preduals of Spaces of Holomorphic Functions

Christopher BOYD

Department of Mathematics
University College Dublin
Belfield, Dublin 4 — Ireland

Received: October 27, 1992
Revised: January 29, 1993

ABSTRACT

For $U$ open in a locally convex space $E$ it is shown in Mújica and Nachbin (1992) that there is a complete locally convex space $G(U)$ such that $G(U)'i = (H(U),td)$ . We will show that when $U$ is balanced there is an $S$ -absolute decomposition for $G(U)$ in terms of the preduals of the spaces of homogeneous polynomials. For $U$ balanced open in a Fréchet space we investigate necessary and sufficient conditions for $(H(U),td)$ to be equal to $' G(U)b$ .

1991 Mathematics Subject Classification: 46G20.