On the Riesz Almost Convergent Sequences Space | Zendy

Mehmet Şengönül | Zendy; Kuddusi Kayaduman | Zendy

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On the Riesz Almost Convergent Sequences Space

Author(s) -

Mehmet Şengönül,

Kuddusi Kayaduman

Publication year - 2012

Publication title -

abstract and applied analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.228

H-Index - 56

eISSN - 1687-0409

pISSN - 1085-3375

DOI - 10.1155/2012/691694

Subject(s) - mathematics , dual polyhedron , sequence (biology) , sequence space , pure mathematics , space (punctuation) , order (exchange) , matrix (chemical analysis) , riesz representation theorem , mathematical analysis , banach space , linguistics , philosophy , genetics , materials science , finance , economics , composite material , biology

The purpose of this paper is to introduce new spaces and 0 that consist of all sequences whose Riesz transforms of order one are in the spaces and 0, respectively. We also show that and 0 are linearly isomorphic to the spaces and 0, respectively. The - and -duals of the spaces and 0 are computed. Furthermore, the classes (∶) and (∶) of infinite matrices are characterized for any given sequence space and determine the necessary and sufficient conditions on a matrix to satisfy −core()⊆−core(), −core()⊆−core() for all ∈ℓ∞

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