Tight J-Frames in Krein Space and the Associated J-Frame Potential
نویسندگان
چکیده
Motivated by the idea of J-frame for a Krein space K , introduced by Giribet et al. (J. I. Giribet, A. Maestripieri, F. Martnez Peŕıa, P. G. Massey, On frames for Krein spaces, J. Math. Anal. Appl. (1), 393 (2012), 122–137.), we introduce the notion of ζ − J-tight frame for a Krein space K . In this paper we characterize J-orthonormal basis for 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 918 Sk. Monowar Hossein et al. provided a necessary and sufficient condition for a J-frame potential of the corresponding ζ − J-tight frame to be minimum. Mathematics Subject Classification: 42C15, 46C05, 46C20
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