Series expansions in Fréchet spaces and their duals, construction of Fréchet frames期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

Series expansions in Fréchet spaces and their duals, construction of Fréchet frames

Authors:	S. Pilipovi? D.T. Stoeva

Affiliation:	^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

Abstract:	Frames for Fréchet spaces X_F with respect to Fréchet sequence spaces Θ_F are studied, and conditions implying series expansions in X_F and are determined. If is a Θ₀-frame for X₀ and Θ_F (resp. X_F) is given, we construct a sequence {X_s}_s∈N₀, X_s⊂X_s−1, s∈N, (resp. {Θ_s}_s∈N₀, Θ_s⊂Θ_s−1, s∈N), so that is a pre-F-frame or F-frame for X_F with respect to Θ_F under different assumptions given on X₀, Θ₀ and Θ_F (resp. X_F).

Keywords:	Banach frame Fré chet frame Pre-Fré chet frame
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