ON A GENERALIZATION OF ATOMIC DECOMPOSITIONS

Abstract

We generalize atomic decomposition for Banach spaces and called it $T$-atomic decomposition. A necessary condition for $T$-atomic decomposition is given. A characterization for a triangular atomic decomposition is also given. Finally, as an application of triangular atomic decompositions, we prove that if a Banach space has a triangular atomic decomposition, then it also has an approximative atomic decomposition, an atomic decomposition and a fusion Banach frame.