Banach Jordan Research Articles

On symmetry of Banach Jordan algebras

Using a very simple subharmonic argument we prove that a Banach Jordan algebra is Hermitian if and only if the sum of two positive elements is positive. We apply this result to give a characterization of Banach Jordan algebras with involution which are J B ∗ J{B^ * } -algebras for an equivalent norm.

The uniqueness of the complete norm topology in Banach algebras and Banach Jordan algebras

In this paper we give a very simple subharmonic proof of an extension of the famous theorem of B. E. Johnson on the equivalence of complete norms in semi-simple Banach algebras. This proof avoids irreducible representations so that it can be adapted to the situation of Banach Jordan algebras in order to give a similar result.

Equivalent norms on Banach Jordan algebras

1. Introduction. Recently Kaplansky suggested the definition of a suitable Jordan analogue of B*-algebras, which we call J B*-algebras (see (10) and (11)). In this article, we give a characterization of those complex unital Banach Jordan algebras which are J B*-algebras in an equivalent norm. This is done by generalizing results of Bonsall ((3) and (4)) to give necessary and sufficient conditions on a real unital Banach Jordan algebra under which it is the self-adjoint part of a J B*-algebra in an equivalent norm. As a corollary we also obtain a characterization of the cones in a Banach Jordan algebra which are the set of positive elements of a J B*-algebra.

Hermitian Operators on Banach Jordan Algebras

In this note, we examine some of the properties of Hermitian operators on complex unital Banach Jordan algebras, that is, those operators with real numerical range. Recall that a unital Banach Jordan algebra J, is a (real or complex) Jordan algebra with product a ˚ b, having a unit 1, and a norm ∥·∥, such that J, with norm ∥·∥, is a Banach space, ∥1∥ = 1, and, for all a and b in j,

A Vidav theorem for Banach Jordan algebras

AbstractIn the present article we prove a result characterizing the Jordan analogues of B*-algebras among the complex Banach Jordan algebras in terms of the algebra and norm structures alone.