atic Continuity of Orthogonality Preserving between C^*-Algebras and von Neumann Algebras on L^P - Spaces

Abstract

We show that every biorthogonality preserving linear surjection between two dual or compact C^*-algebras or between two von Neumann algebras is automatically continuous . Consequently, every complete (semi-norm on a von Neumann algebra or on a compact C^*-algebra is automatically continuous .We study orthogonality preserving surjective linear maps from a unital C^*-algebra with non-zero socle to a C^*-algebra . We show that an orthogonality-to-p-orthogonality preserving linear bijection from the Lebesque space to a Banach space is automatically continuous, whenever the von Neumann algebra is a separably acting von Neumann algebra.