@article{Kumar_Joshi_Singh_Sah_2014, title={Construction of generalized atomic decompositions in Banach spaces}, volume={2}, url={https://sciencepubco.com/index.php/IJAMS/article/view/2783}, DOI={10.14419/ijams.v2i3.2783}, abstractNote={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.}, number={3}, journal={International Journal of Advanced Mathematical Sciences}, author={Kumar, Raj and Joshi, Mahesh and Singh, Ram and Sah, Ashok}, year={2014}, month={Jun.}, pages={116–124} }