IJPAM: Volume 66, No. 3 (2011)

A HELLY TYPE THEOREM IN THE SETTING OF
BANACH SPACES

Miloslav Duchon
Mathematical Institute
Slovak Academy of Sciences
49, Štefánikova, Bratislava, SK-814 73, SLOVAKIA
e-mail: miloslav.duchon@mat.savba.sk


Abstract.There is given an extension of the classical Helly and Helly-Bray Theorems to functions with values in Banach spaces. An application is given to a moment problem. From this, a representation theorem for compact mappings of the space of continuous functions into a Banach space is derived.

Received: November 10, 2010

AMS Subject Classification: 28E10, 81P10

Key Words and Phrases: semivariation, vector Riemann-Stieltjes integral, (weakly) compact operator, moment

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2011
Volume: 66
Issue: 3