Characterizations of Compact Operators on ℓ_p Type Fractional Sets of Sequences

2018/02/12 by Faruk Özger, Özger, Faruk
Mathematics · #46B45 #47B37 #FOS: Mathematics #Functional Analysis (math.FA) #math.FA #msc:46B45 #msc:47B37

paper · pdf · doi:10.48550/arxiv.1802.04081

13 pages

arxiv created 2018/02/12 · arxiv updated 2018/02/13

Abstract

Among the sets of sequences studied, difference sets of sequences are probably the most common type of sets. This paper considers some ℓ_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 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.

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