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arXiv · 1609.08659

Tight J-frames in Krein space and the associated J-frame potential

Sk. Monowar Hossein·Shibashis Karmakar·Kallol Paul
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Abstract

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. Martínez Pería, P. G. Massey, \textit{On frames for Krein spaces}, J. Math. Anal. Appl. (1), {\bf 393} (2012), 122--137.), we introduce the notion of $ζ-J$-tight frame for a Krein space $\textbf{\textit{K}}$. In this paper we characterize $J$-orthonormal basis for $\textbf{\textit{K}}$ in terms of $ζ-J$-Parseval frame. We show that a Krein space is richly supplied with $ζ-J$-Parseval frames. We also provide a necessary and sufficient condition when the linear sum of two $ζ-J$-Parseval frames is again a $ζ-J$-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 $ζ-J$-tight frame to be minimum.

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Sk. Monowar Hossein, Shibashis Karmakar, Kallol Paul. 2016-09-27. Tight J-frames in Krein space and the associated J-frame potential. https://doi.org/10.12988/ijma.2016.6355

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