S-g-sequences and the conditions for invertibility of multiplier operator

Document Type: Research Paper




Frame theory is a research topic that is a useful and exact tool in solving various applied problems and the related branch to mathematics. Multiplier operator plays an important role in the above subjects. In this regard, the multiplier operator is studied in these pages. The paper presents sufficient conditions for invertibility of multiplier operator corresponding to s-g-frames, s-g-Riesz bases, and s-g-orthonormal basis, and obtains its inverse operator. Moreover, according to the relation between s-g-frames and generalized frames, we try to consider some sufficient conditions for the invertibility property of a g-frame multiplier operator.