Construction of generalized atomic decompositions in Banach spaces

  • Authors

    • Raj Kumar Department of Mathematics Kirori mal college University of Delhi Delhi-110007 India.
    • Mahesh Joshi Professor DEPARTMENT OF MATHEMATICS, D.S.B,CAMPUS ,Kumaun University. NAINITAL-263001, INDIA
    • Ram Singh DEPARTMENT OF MATHEMATICS, D.S.B,CAMPUS ,Kumaun University. NAINITAL-263001, INDIA
    • Ashok Sah Department of Mathematics Kirori mal college University of Delhi Delhi-110007 India.
    2014-06-15
    https://doi.org/10.14419/ijams.v2i3.2783
  • 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.

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    Kumar, R., Joshi, M., Singh, R., & Sah, A. (2014). Construction of generalized atomic decompositions in Banach spaces. International Journal of Advanced Mathematical Sciences, 2(3), 116-124. https://doi.org/10.14419/ijams.v2i3.2783