2024/11/12 by Najib Khachiaa, Khachiaa, Najib
Mathematics · #42C15 #42C40 #47A05 #Advanced Mathematical Physics Problems #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods
paper · pdf · doi:10.48550/arxiv.2411.07937
openalex publication_date 2024/11/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper aims to explore the concept of continuous \( K \)-frames in quaternionic Hilbert spaces. First, we investigate \( K \)-frames in a single quaternionic Hilbert space \( H \), where \( K \) is a right ℍ-linear bounded operator acting on \( H \). Then, we extend the research to two quaternionic Hilbert spaces, \( H1 \) and \( H2 \), and study \( K1 ⊕ K2 \)-frames for the super quaternionic Hilbert space \( H1 ⊕ H2 \), where \( K1 \) and \( K2 \) are right ℍ-linear bounded operators on \( H1 \) and \( H2 \), respectively. We examine the relationship between the continuous \( K1 ⊕ K2 \)-frames and the continuous \( K1 \)-frames for \( H1 \) and the continuous \( K2 \)-frames for \( H2 \). Additionally, we explore the duality between the continuous \( K1 ⊕ K2 \)-frames and the continuous \( K1 \)- and \( K2 \)-frames individually.