Series expansions in Fréchet spaces and their duals, construction of Fréchet frames
نویسندگان
چکیده
Frames for Fréchet spaces XF with respect to Fréchet sequence spaces ΘF are studied and conditions, implying series expansions in XF and X ∗ F , are determined. If {gi}i=1 is a Θ0-frame for X0, we construct a sequence {Xs}s∈N0 , Xs ⊂ Xs−1, s ∈ N, for given ΘF , respectively a sequence {Θs}s∈N0 , Θs ⊂ Θs−1, s∈N, for given XF , so that {gi}i=1 is a pre-F -frame (or F -frame) for XF with respect to ΘF under different assumptions given on X0, Θ0, ΘF or X0, Θ0, XF .
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ورودعنوان ژورنال:
- Journal of Approximation Theory
دوره 163 شماره
صفحات -
تاریخ انتشار 2011