An algebraic closed graph theorem

Gabriel Michael Miller Obi

Vol. 74 (1978), No. 1, 199–207

DOI: 10.2140/pjm.1978.74.199

Abstract

In this work we consider the question as to when an everywhere defined closed linear map from a quadratic space H₁ into another such space H₂ is orthocontinuous. The following result is proved:

Let (H₁,Φ₁), (H₂,Φ₂) be quadratic spaces whose ⊥-closed subspaces are semi-simple. If T is an everywhere defined closed linear map on H₁ into H₂ then T is orthocontinuous.

Mathematical Subject Classification 2000

Primary: 46A30

Secondary: 46C10

Milestones

Received: 17 May 1977

Published: 1 January 1978