Characterizations of Compact Operators on $\ell_{p}$ Type Fractional Sets of Sequences

Faruk Özger

Published 2018-02-12Version 1

Among the sets of sequences studied, difference sets of sequences are probably the most common type of sets. This paper considers some $\ell_{p}$ type fractional difference sequence spaces via Euler gamma function. Although we characterize compactness conditions on those spaces using the main tools of Hausdorff measure of noncompactness, we can only obtain sufficient conditions when the final space is $\ell _{\infty }$. However, we use some recent results to exactly characterize the classes of compact matrix operators when the final space is the set of bounded sequences.