Atomic subspaces for operators

This paper introduces the concept of atomic subspaces with respect to a bounded linear operator. Atomic subspaces generalize fusion frames and this generalization leads to the notion of $K$-fusion frames. Characterizations of $K$-fusion frames are discussed. Various properties of $K$-fusion frames, for example, direct sums, intersection, are studied.
Comment: 11 pages, To appear in Indian Journal of Pure and Applied Mathematics (2020)