Supporting sequences of pure states on JB algebras

CHEBYSHEV SUBALGEBRAS OF JB-ALGEBRAS

In this note, we characterize Chebyshev subalgebras of unital JB-algebras. We exhibit that if B is Chebyshev subalgebra of a unital JB-algebra A, then either B is a trivial subalgebra of A or A= H R .l, where H is a Hilbert space

Automatic Continuity of Higher Derivations on JB*-Algebras

On Continuous Fields of Jb-algebras

We introduce and study continuous fields of JB-algebras (which are real non-associate analogues of C*-algebras). In particular, we show that for the universal enveloping C*-algebra C∗ u (B) for the JB-algebra B defined by a continuous field of JB-algebras At, t ∈ T, on a locally compact space T there exists a decomposition of C∗ u (B) into a continuous field of C*-algebras C∗ u (At), t ∈ T, on ...

Generalized states on EQ-algebras

In this paper, we introduce a notion of generalized states from an EQ-algebra E1 to another EQ-algebra E2, which is a generalization of internal states (or state operators) on an EQ-algebra E. Also we give a type of special generalized state from an EQ-algebra E1 to E1, called generalized internal states (or GI-state). Then we give some examples and basic properties of generalized (internal) st...

Geometric Unitaries in Jb-algebras

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...