Controlled g-Atomic Subspaces for Operators in Hilbert Spaces

Abstract

A controlled $$g$$ -atomic subspace for a bounded linear operator is presented and a characterization has been given. We give an example of controlled $$K$$ - $$g$$ -fusion frame. We construct a new controlled $$K$$ - $$g$$ -fusion frame for the Hilbert space $$H \oplus X$$ using the controlled $$K$$ - $$g$$ -fusion frames of Hilbert spaces $$H$$ and $$X$$ . Several useful resolutions of the identity operator on a Hilbert space using the theory of controlled $$g$$ -fusion frames have been discussed. We introduce the frame operator for a pair of controlled $$g$$ -fusion Bessel sequences.