Phép Kéo Dãn của Các Khung Hilbert–Schmidt (Đối)

Springer Science and Business Media LLC - Tập 13 - Trang 1-20 - 2022
Yun-Zhang Li1, Xiao-Li Zhang1
1Department of Mathematics, Faculty of Science, Beijing University of Technology, Beijing, People’s Republic of China

Tóm tắt

Bài báo này đề cập đến vấn đề phép kéo dãn trên các khung Hilbert–Schmidt (HS-frames) (đối khung). Chúng tôi trình bày một định lý kéo dãn từ một khung HS (khung HS Parseval, cặp khung HS đối) tới một cơ sở HS–Riesz (cơ sở HS-orthonormal, cặp cơ sở HS–Riesz đối) và chứng minh rằng khung HS-ortogonal bổ sung tương ứng (khung HS bổ sung chung) là duy nhất với điều kiện tương đương (tương đương đơn vị, tương đương chung). Một ghi chú cũng được cung cấp, cho thấy rằng kết quả và phương pháp của chúng tôi có thể khôi phục một số kết quả kéo dãn hiện có về các khung và g-khung.

Từ khóa

#khung Hilbert–Schmidt #phép kéo dãn #cơ sở HS–Riesz #tiên đề Parseval #khung bổ sung #tương đương đơn vị

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