Criteria for Banach spaces

Joseph Earl Valentine and Stanley G. Wayment

Vol. 43 (1972), No. 1, 251–252

DOI: 10.2140/pjm.1972.43.251

Abstract

It is well known in euclidean geometry that the quadrilateral obtained from an arbitrary quadrilateral by joining its midpoints is a parallelogram. The purpose of this paper is to show that a complete metric space with a unique metric line joining any pair of its distinct points is a Banach space if and only if it has the above mentioned property.

Mathematical Subject Classification 2000

Primary: 46B10

Milestones

Received: 16 August 1971

Published: 1 October 1972