Year: 2025
Type: article
Abstract: The contributions in this note begin with a new characterization of (positive) scalar multiples of minimal tripotents in a general $$\hbox {JB}^*$$ JB ∗ -triple E, proving that a non-zero element $$a\in E$$ a ∈ E is a positive scalar multiple of a minimal tripotent in E if, and only if, its inner quadratic annihilator (that is, the set $$\phantom {a}^{\perp _{q}}\{a\} = \{ b\in E: \{a,b,a\} =0\}$$ a ⊥ q { a } = { b ∈ E : { a , b , a } = 0 } ) is maximal among all inner quadratic annihilators of single elements in E. We subsequently apply this characterization to the study of surjective additive maps between atomic $$\hbox {JBW}^*$$ JBW ∗ -triples preserving truncations in both directions. Assume that $$E = \bigoplus _{k\in \Gamma _1}^{\ell _{\infty }} C_k$$ E = ⨁ k ∈ Γ 1 ℓ ∞ C k and $$F = \bigoplus _{{j\in \Gamma _2}}^{\ell _{\infty }} \widetilde{C}_j$$ F = ⨁ j ∈ Γ 2 ℓ ∞ C ~ j , are two atomic JBW $$^*$$ ∗ -triples, where $$\{C_k\}_{k\in \Gamma _1}$$ { C k } k ∈ Γ 1 and $$\{\widetilde{C}_j\}_{j\in \Gamma _2}$$ { C ~ j } j ∈ Γ 2 are two families of Cartan factors. Let $$A: E\rightarrow F$$ A : E → F be a surjective additive mapping between atomic $$\hbox {JBW}^*$$ JBW ∗ -triples, where E contains
Authors: Lei Li, Siyu Liu, Antonio M. Peralta
Institutions: Nankai University, Universidad de Granada
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,190
OpenAlex ID: W4411777859