Research Article
Characterizations of the semi-harmonious and harmonious quasi-projection pairs on Hilbert C
∗-modules
DOI:
10.2989/16073606.2025.2550026
Author(s):
Xiaoyi Tian Shanghai Normal University, P.R. China, Qingxiang Xu Shanghai Normal University, P.R. China, Chunhong Fu Health School Attached to Shanghai University of Medicine & Health Sciences, P.R. China,
Abstract
For each adjointable idempotent Q on a Hilbert C
∗ -module , a specific projection m(Q) called the matched projection of Q was introduced recently due to the characterization of the minimum value among all the distances from projections to Q. Inspired by the relationship between m(Q) and Q, another term called the quasi-projection pair (P, Q) was also introduced recently, where P is a projection on satisfying Q
∗ = (2P − I )Q(2P − I ), in which Q
∗ is the adjoint operator of the idempotent Q and I is the identity operator on . This paper aims to make systematical characterizations of the semi-harmonious and harmonious quasi-projection pairs on Hilbert C
∗ -modules, and meanwhile to provide examples illustrating the non-triviality of the associated characterizations.
Get new issue alerts for Quaestiones Mathematicae
