State automorphisms in axiomatic quantum mechanics

Abstract

A new metric which we call the ‘intrinsic metric’ is introduced on the statesℐ of the generalized logic of quantum mechanics. It is shown that every automorphism onℐ is an isometry. A norm can be defined on the linear spanE ofℐ which reduces to the intrinsic metric onℐ. IfX is the completion ofE then every automorphism, onℐ has a unique extension to a linear isometry onX. A comparison is made between these results and those of Kroniff.