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Convexity characteristic of Calderón–Lozanovskiĭ sequence spaces
Author(s) -
Yan Yaqiang,
Hou Zhentao
Publication year - 2014
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201200170
Subject(s) - mathematics , sequence (biology) , convexity , monotone polygon , sequence space , measure (data warehouse) , space (punctuation) , regular polygon , order (exchange) , pure mathematics , combinatorics , convex function , lorentz transformation , function (biology) , continuous function (set theory) , mathematical analysis , geometry , banach space , linguistics , philosophy , genetics , physics , finance , classical mechanics , database , evolutionary biology , computer science , financial economics , economics , biology
Hudzik, Kamińska and Mastyło obtained some geometric properties of Calderón–Lozanovskiĭ function spaces which are defined on a nonatomic σ‐measure space ( Ω , Σ , μ ) in Houston. J. Math. 22 (1996), but left the case of atomic measure unsolved. We studied the relevant problems for the sequence spaces and obtained the following main results: For the Calderón–Lozanovskiĭ sequence spacese Φ , e Φis order continuous if and only ifΦ ∈ δ 2and e is order continuous . Let Φ be strictly convex on[ 0 , u b ] , then the convex characteristicε 0 ( e Φ ) = 2whenever e is not order continuous orΦ ∉ δ 2 ; if e is uniformly monotone andΦ ∈ δ 2 , thenε 0 ( e Φ ) ≤ 2 ( 1 − p ( Φ ) ) 1 + p ( Φ ). For the Orlicz‐Lorentz sequence spaceλ Φ , ω ,ε 0 ( λ Φ , ω ) = 2ifΦ ∉ δ 2orΨ ∉ δ 2 , or ω is not regular ;ε 0 ( λ Φ , ω ) = 2 ( 1 − p ( Φ ) ) 1 + p ( Φ )if Φ is strictly convex on0 , Φ − 11 ω 1, Φ ∈ δ 2and ω is regular .