English

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.

Keywords

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}
}