Some Compact Operators on the Hahn Space | Zendy

Eberhard Malkowsky | Zendy

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Some Compact Operators on the Hahn Space

Author(s) -

Eberhard Malkowsky

Publication year - 2021

Publication title -

scientific research communications

Language(s) - English

Resource type - Journals

ISSN - 2791-8742

DOI - 10.52460/src.2021.001

Subject(s) - bounded function , mathematics , sequence (biology) , measure (data warehouse) , bounded operator , monotone polygon , zero (linguistics) , space (punctuation) , pure mathematics , linear operators , compact space , operator theory , compact operator , discrete mathematics , mathematical analysis , extension (predicate logic) , computer science , linguistics , philosophy , genetics , geometry , database , biology , operating system , programming language

We establish the characterisations of the classes of bounded linear operators from the generalised Hahn sequence space hd, where d is an unbounded monotone increasing sequence of positive real numbers, into the spaces [c0], [c] and [c1] of sequences that are strongly convergent to zero, strongly convergent and strongly bounded. Furthermore, we prove estimates for the Hausdor_ measure of noncompactness of bounded linear operators from hd into [c], and identities for the Hausdor_ measure of noncompactness of bounded linear operators from hd to [c0], and use these results to characterise the classes of compact operators from hd to [c] and [c0].

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