Geometric Unitaries in Jb-algebras
نویسنده
چکیده
In this article, we study geometric unitaries of JB-algebras (in particular, self-adjoint parts of C∗-algebras). We will show that the geometric unitaries of a JB algebra are precisely those central algebraic unitaries (or central symmetries). We will also show that the group of surjective isometries on a JB-algebra A (with point-norm topology) is the semi-direct product of the canonical action of its Jordan automorphism group (with point-norm topology) on the group of geometric unitaries of M(A) (with the strict topology). As a consequence, a continuous isometric action of a connected group on a unital JB-algebra is automatically an action by Jordan automorphisms (without knowing a priori that those isometries preserve the identity).
منابع مشابه
Convex combinations of unitaries in JB∗-algebras
We continue our recent efforts to exploit the notion of a unitary isotope to study convex combinations of unitaries in an arbitrary JB∗-algebra. Exact analogues of C∗-algebraic results, due to R. V. Kadison, C. L. Olsen and G. K. Pedersen, are proved for general JB∗-algebras. We show that if a contraction in a JB∗-algebra is a convex combination of n unitaries, then it is also a mean of n unita...
متن کاملAsymmetric Decompositions of Vectors in Jb∗-algebras
By investigating the extent to which variation in the coefficients of a convex combination of unitaries in a unital JB-algebra permits that combination to be expressed as convex combination of fewer unitaries of the same algebra, we generalise various results of R. V. Kadison and G. K. Pedersen. In the sequel, we shall give a couple of characterisations of JB-algebras of tsr
متن کاملJB*-Algebras of Topological Stable Rank 1
In 1976, Kaplansky introduced the class JB∗-algebras which includes all C∗-algebras as a proper subclass. The notion of topological stable rank 1 for C∗-algebras was originally introduced by M. A. Rieffel and was extensively studied by various authors. In this paper, we extend this notion to general JB∗-algebras. We show that the complex spin factors are of tsr 1 providing an example of special...
متن کاملOn Unitary Convex Decompositions of Vectors in a Jb∗-algebra
By exploiting his recent results, the author further investigates the extent to which variation in the coefficients of a unitary convex decomposition of a vector in a unital JB∗-algebra permits the vector decomposable as convex combination of fewer unitaries; certain C∗-algebra results due to M. Rørdam have been extended to the general setting of JB∗-algebras.
متن کامل