Jordan operator algebras: basic theory

Jordan Maps on Standard Operator Algebras

Jordan isomorphisms of rings are defined by two equations. The first one is the equation of additivity while the second one concerns multiplicativity with respect to the so-called Jordan product. In this paper we present results showing that on standard operator algebras over spaces with dimension at least 2, the bijective solutions of that second equation are automatically additive.

Operator Theory and Operator Algebras

Multiplicity Theory for Operator Algebras.

I Since (3.1) is homogeneous of degree zero in vm, vm, and am in (3.2) can be taken to be dym/dy4, d2y/(dy4)2,resp. Thenv4 = 1 a4= 0 10 On the nullspheres (X = 0) one gets If = 0, where R = 0-i.e., just the Coulomb infinity. 11 E.g., X acts like a sort of gauge, or numerical length assigned to some standard physical rod by the observer at xm. This rod can be assigned any positive value, but not...

Löwner's Operator and Spectral Functions in Euclidean Jordan Algebras

We study analyticity, differentiability, and semismoothness of Löwner’s operator and spectral functions under the framework of Euclidean Jordan algebras. In particular, we show that many optimization-related classical results in the symmetric matrix space can be generalized within this framework. For example, the metric projection operator over any symmetric cone defined in a Euclidean Jordan a...

Deformation of central charges, vertex operator algebras whose Griess algebras are Jordan algebras

If a vertex operator algebra V = ⊕n=0Vn satisfies dimV0 = 1, V1 = 0, then V2 has a commutative (nonassociative) algebra structure called Griess algebra. One of the typical examples of commutative (nonassociative) algebras is a Jordan algebra. For example, the set Symd(C) of symmetric matrices of degree d becomes a Jordan algebra. On the other hand, in the theory of vertex operator algebras, cen...