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arXiv · 1511.08420

Orthogonal forms and orthogonality preservers on real function algebras revisited

Antonio M. Peralta
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Abstract

In 2014, we determine the precise form of a continuous orthogonal form on a commutative real C$^*$-algebra. We also describe the general form of a (not-necessarily continuous) orthogonality preserving linear map between commutative unital real C$^*$-algebras. Among the consequences, we show that every orthogonality preserving linear bijection between commutative unital real C$^*$-algebras is continuous. In this note we revisit these results and their proofs with the idea of filling a gap in the arguments, and to extend the original conclusions.

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Antonio M. Peralta. 2015-11-26. Orthogonal forms and orthogonality preservers on real function algebras revisited. https://arxiv.org/abs/1511.08420

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