Characterizations of compact operators on ℓp−type fractional sets of sequences

Abstract

Among the sets of sequences studied, difference sets of sequences are probably the most common type of sets. This paper considers some ℓp−type fractional difference sets via the gamma function. Although, we characterize compactness conditions on those sets using the main key of Hausdorff measure of noncompactness, we can only obtain sufficient conditions when the final space is ℓ∞. 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.

Keywords

• gamma function
• fractional operator
• operator norm
• compact operator
• hausdorff measure of noncompactness
• 46b45
• 47b37