Maps completely preserving indefinite Jordan 1-†-zero product

Abstract

By characterizing the bijections preserving orthogonality of idempotents in both directions on the infinite dimensional complete indefinite inner product spaces, we obtain the concrete form of surjective maps completely preserving indefinite Jordan 1-†-zero product between †-standard operator algebras. Our results show that such maps are nonzero constant multiple of isomorphisms or conjugate isomorphisms.

Keywords

†-standard operator algebras / complete preserving problem / indefinite inner product spaces / indefinite Jordan 1-†-zero product

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