Year: 2025
Type: article
Abstract: Let Asem = {A ∈ A : Re A = A∗A} be the set of all semiorthogonal projections of the unital C∗-algebra A, I be the identity of A. The formula U = 2A − I (A ∈ Asem) defines a bijection between the set Asem and the set of all isometries from A. For any natural number n ≥ 2, there exists a non-commutative polynomial of degree n that yields a semi-orthogonal projection when substituted for an arbitrary set A1, . . . , An ∈ Asem. Each element A ∈ Asem is hyponormal and lies in the unit ball of the C∗-algebra A. If A ∈ Asem, then A2 is hyponormal. If A, A2 ∈ Asem, then A is a projection. If A ∈ Asem and A = An for some n ∈ N, n ≥ 2, then A is a normal element, and A is a projection for n = 2.
Author: A. M. Bikchentaev
Institution: Kazan Federal University
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
OpenAlex ID: W4412674337