Series expansions in Fréchet spaces and their duals, construction of Fréchet frames |
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| Authors: | S Pilipovi? DT Stoeva |
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| Institution: | aDepartment of Mathematics and Informatics, University of Novi Sad, Trg D. Obradovi?a 4, 21000 Novi Sad, Serbia;bDepartment of Mathematics, University of Architecture, Civil Engineering and Geodesy, Blvd Hristo Smirnenski 1, 1046 Sofia, Bulgaria |
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| Abstract: | Frames for Fréchet spaces XF with respect to Fréchet sequence spaces ΘF are studied, and conditions implying series expansions in XF and  are determined. If  is a Θ0-frame for X0 and ΘF (resp. XF) is given, we construct a sequence {Xs}s∈N0, Xs⊂Xs−1, s∈N, (resp. {Θs}s∈N0, Θs⊂Θs−1, s∈N), so that  is a pre-F-frame or F-frame for XF with respect to ΘF under different assumptions given on X0, Θ0 and ΘF (resp. XF). |
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| Keywords: | Banach frame Fré chet frame Pre-Fré chet frame |
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