2024/11/06 by Najib Khachiaa, Khachiaa, Najib
Mathematics · Physics and Astronomy · #42C15 #42C40 #47A05 #Advanced Differential Geometry Research #Algebraic and Geometric Analysis #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods
paper · pdf · doi:10.48550/arxiv.2411.04154
openalex publication_date 2024/11/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The aim of this paper is to study K-frames for quaternionic Hilbert spaces. First, we present the quaternionic version of Douglas's theorem and then investigate K-frames for a quaternionic Hilbert space H, where K ∈ \mathbbB(H). Given two quaternionic Hilbert spaces H1 and H2, along with two right ℍ-linear bounded operators K1 ∈ \mathbbB(H1) and K2 ∈ \mathbbB(H2), we study the K1 ⊕ K2-frames for the super space H1 ⊕ H2 and their relationship with K1-frames and K2-frames for H1 and H2, respectively. We also explore the K1 ⊕ K2-duality in relation to K1-duality and K2-duality.