Enlargements of quantum logics

Mirko Navara, Pavel Pták and Vladimír Rogalewicz

Vol. 135 (1988), No. 2, 361–369

DOI: 10.2140/pjm.1988.135.361

Abstract

Let K be a quantum logic whose state space is nonvoid. Let B be a Boolean algebra and let C be a compact convex subset of a locally convex topological linear space. Then K can be enlarged to a logic L such that the centre of L equals B and the state space of L equals C. (The result remains valid when we replace the word “logic” with “orthomodular lattice”.)

Mathematical Subject Classification 2000

Primary: 03G12

Secondary: 81B10, 46N05

Milestones

Received: 10 June 1987

Published: 1 December 1988