Year: 2025
Type: article
Abstract: We show in this paper Gudder–Nagy’s theorem for operators on Hilbert C ∗ ‐modules over C ∗ ‐algebra of compact operators. Let H be a complex Hilbert space with dim H > 1, and K ( H ) the C ∗ ‐algebra of compact operators on H . For bounded K ( H )‐linear operators A , B and C on Hilbert C ∗ ‐module X over K ( H ), we show that 〈 A x , x 〉〈 B x , x 〉 = 〈 x , x 〉〈 C x , x 〉, for all x ∈ X , if and only if there is a complex number λ such that A = λ I and C = λ B .
Source: Journal of Mathematics
DOI: 10.1155/jom/3623110
Author: Ming-Hsiu Hsu
Institution: Feng Chia University
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $2,160
OpenAlex ID: W4413182467