Equivalent norms in ${{\mathbb{R}}}^{n}$ from thermodynamical laws

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.

Download Full-text

Multi-Sourced Equivalent Norms and the Legitimacy of Indigenous Peoples’ Rights under International Law

Multi-Sourced Equivalent Norms in International Law ◽

10.5040/9781472565457.ch-012 ◽

2014 ◽

Keyword(s):

International Law ◽

Indigenous Peoples ◽

Equivalent Norms

Download Full-text

Interpreting Multi-Sourced Equivalent Norms : Judicial Borrowing in International Courts

Multi-Sourced Equivalent Norms in International Law ◽

10.5040/9781472565457.ch-005 ◽

2014 ◽

Cited By ~ 1

Keyword(s):

International Courts ◽

Equivalent Norms

Download Full-text

Best Constants for the Inequalities between Equivalent Norms in Orlicz Spaces

Bulletin of the Polish Academy of Sciences Mathematics ◽

10.4064/ba59-2-6 ◽

2011 ◽

Vol 59 (2) ◽

pp. 165-174

Author(s):

Ha Huy Bang ◽

Nguyen Van Hoang ◽

Vu Nhat Huy

Keyword(s):

Orlicz Spaces ◽

Best Constants ◽

Equivalent Norms

Download Full-text

A Dual characterization of Banach Spaces With the Convex Point-of-Continuity Property

Canadian Mathematical Bulletin ◽

10.4153/cmb-1989-040-0 ◽

1989 ◽

Vol 32 (3) ◽

pp. 274-280

Author(s):

D. E. G. Hare

Keyword(s):

Banach Spaces ◽

Continuity Property ◽

Dual Spaces ◽

Equivalent Norms ◽

Fréchet Differentiability ◽

New Type ◽

Frechet Differentiability ◽

Point Of Continuity Property ◽

Convex Point

AbstractWe introduce a new type of differentiability, called cofinite Fréchet differentiability. We show that the convex point-of-continuity property of Banach spaces is dual to the cofinite Fréchet differentiability of all equivalent norms. A corresponding result for dual spaces with the weak* convex point-of-continuity property is also established.

Download Full-text