Displaying similar documents to “On the Lebesgue decomposition of the normal states of a JBW-algebra”

Espacios de producto interno (II).

Palaniappan Kannappan (1995)

Mathware and Soft Computing

Similarity:

Among normal linear spaces, the inner product spaces (i.p.s.) are particularly interesting. Many characterizations of i.p.s. among linear spaces are known using various functional equations. Three functional equations characterizations of i.p.s. are based on the Frchet condition, the Jordan and von Neumann identity and the Ptolemaic inequality respectively. The object of this paper is to solve generalizations of these functional equations.

Pure states on Jordan algebras

Jan Hamhalter (2001)

Mathematica Bohemica

Similarity:

We prove that a pure state on a C * -algebras or a JB algebra is a unique extension of some pure state on a singly generated subalgebra if and only if its left kernel has a countable approximative unit. In particular, any pure state on a separable JB algebra is uniquely determined by some singly generated subalgebra. By contrast, only normal pure states on JBW algebras are determined by singly generated subalgebras, which provides a new characterization of normal pure states. As an application...