| Autor: |
Hossein, Sk. Monowar, Karmakar, Shibashis, Paul, Kallol |
| Rok vydání: |
2016 |
| Předmět: |
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| Zdroj: |
IJMA, Vol.10, 2016, no.19, 917-931 |
| Druh dokumentu: |
Working Paper |
| DOI: |
10.12988/ijma.2016.6355 |
| Popis: |
Motivated by the idea of $J$-frame for a Krein space $\textbf{\textit{K}}$, introduced by Giribet \textit{et al.} (J. I. Giribet, A. Maestripieri, F. Mart\'inez Per\'{i}a, P. G. Massey, \textit{On frames for Krein spaces}, J. Math. Anal. Appl. (1), {\bf 393} (2012), 122--137.), we introduce the notion of $\zeta-J$-tight frame for a Krein space $\textbf{\textit{K}}$. In this paper we characterize $J$-orthonormal basis for $\textbf{\textit{K}}$ in terms of $\zeta-J$-Parseval frame. We show that a Krein space is richly supplied with $\zeta-J$-Parseval frames. We also provide a necessary and sufficient condition when the linear sum of two $\zeta-J$-Parseval frames is again a $\zeta-J$-Parseval frame. We then generalize the notion of $J$-frame potential in Krein space from Hilbert space frame theory. Finally we provided a necessary and sufficient condition for a $J$-frame potential of the corresponding $\zeta-J$-tight frame to be minimum. |
| Databáze: |
arXiv |
| Externí odkaz: |
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