Year: 2025
Type: article
Abstract: A method is proposed for constructing idempotents in a unital algebra 𝒜 using n arbitrary idempotents P1, . . . , Pn from this algebra. The properties of the resulting idempotents P= P(P1, . . . , Pn); are investigated; for n = 2 and n = 3, explicit forms of the idempotents are obtained: 𝐴(P1, P2) and B(P1, P2, P3), respectively. It is shown that the mappings P2 ↦→ 𝐴(P1, P2), f(P2) = 𝐴(P1, P2) и P3 ↦→ B(P1, P2, P3), g(P3) = B(P1, P2, P3) preserve the complements ⊥ and are multiplicative on wide classes of idempotent pairs. For a finite trace 𝜙 on a unital C* -algebra 𝒜, 𝜙(P(P1, . . . , Pn)) = 𝜙(Pn). For the projections P1, . . . , Pn from the von Neumann algebra 𝒜, the method yields a new projection and enables the construction of some partial isometries.
Author: M. Khadour
Institution: Kazan Federal University
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4412526113