A proof of the Russo–Dye theorem for JB∗-algebras

On 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.

Automatic Continuity of Higher Derivations on JB*-Algebras

A new proof for the Banach-Zarecki theorem: A light on integrability and continuity

To demonstrate more visibly the close relation between thecontinuity and integrability, a new proof for the Banach-Zareckitheorem is presented on the basis of the Radon-Nikodym theoremwhich emphasizes on measure-type properties of the Lebesgueintegral. The Banach-Zarecki theorem says that a real-valuedfunction $F$ is absolutely continuous on a finite closed intervalif and only if it is continuo...

Extremal Positive Solutions For The Distributed Order Fractional Hybrid Differential Equations

In this article, we prove the existence of extremal positive solution for the distributed order fractional hybrid differential equation$$int_{0}^{1}b(q)D^{q}[frac{x(t)}{f(t,x(t))}]dq=g(t,x(t)),$$using a fixed point theorem in the Banach algebras. This proof is given in two cases of the continuous and discontinuous function $g$, under the generalized Lipschitz and Caratheodory conditions.

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