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arXiv · 2506.04412

Maps preserving the idempotency of Jordan products

Tatjana Petek·Gordana Radić
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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.

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Tatjana Petek, Gordana Radić. 2025-06-04. Maps preserving the idempotency of Jordan products. https://arxiv.org/abs/2506.04412

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