Maps preserving the idempotency of Jordan products
Functional Analysis
2025-06-06 v1 Operator Algebras
Abstract
Let B(X) be the algebra of all bounded linear operators on a complex Banach space X of dimension at least three. For an arbitrary nonzero complex number t we determine the form of mappings f: B(X)-->B(X) with sufficiently large range such that t(AB+BA) is idempotent if and only if t(f(A)f(B)+f(B)f(A)) is idempotent, for all A, B in B(X). Note that f is not assumed to be linear or additive.
Cite
@article{arxiv.2506.04412,
title = {Maps preserving the idempotency of Jordan products},
author = {Tatjana Petek and Gordana Radić},
journal= {arXiv preprint arXiv:2506.04412},
year = {2025}
}