%0 Journal Article %T Construction of generalized atomic decompositions in Banach spaces %A Ashok Sah %A Mahesh Joshi %A Raj Kumar %A Ram Singh %J - %D 2014 %R 10.14419/ijams.v2i3.2783 %X G-atomic decompositions for Banach spaces with respect to a model space of sequences have been introduced and studied as a generalization of atomic decompositions. Examples and counter example have been provided to show its existence. It has been proved that an associated Banach space for G-atomic decomposition always has a complemented subspace. The notion of a representation system is introduced and exhibits its relation with G-atomic decomposition. Also It has been observed that G-atomic decompositions are exactly compressions of Schauder decompositions for a larger Banach space. We give a characterization for finite G-atomic decomposition in terms of finite-dimensional expansion of identity. Keywords: complemented coefficient spaces, finite-dimensional expansion of identity, G-atomic decomposition, representation system. %U https://www.sciencepubco.com/index.php/IJAMS/article/view/2783