We introduce the Jordan-strict topology on the multipliers algebra of a JB*-algebra. In case that a C*-algebra $A$ is regarded as a JB*-algebra, the J-strict topology of $M(A)$ is precisely the well-studied C*-strict topology. We prove that every JB*-algebra A is J-strict dense in its multipliers algebra $M(A)$, and that the latter algebra is J-strict complete. We show that continuous surjective Jordan homomorphisms, triple homomorphisms, and orthogonality preserving operators between JB*-algebras admit J-strict continuous extensions to the corresponding type of operators between the multipliers algebras. We show that, under some additional hypothesis this extension is surjective.
Date and Venue
Universidad Politécnica de Madrid
Algebra, Combinatorics and Number Theory