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Dergiler / Hacettepe Journal of Mathematics and Statistics / 2022 / Cilt: 51 - Sayı: 2

A note on topologically b-order bounded sets and generalized b-weakly compact operators

Nabil MACHRAFI
Birol ALTIN
Sayfa
483–493
Yayın Tarihi
2022-04-01
DOI
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

We prove as a consequence that some well-known results on $b$-weakly compact operators on a Banach lattice extend in an improved version to generalized $b$-weakly compact operators on a Fréchet lattice.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:We study the class of order weakly compact operators on locally solid Riesz spaces and the introduced class of generalized $b$-weakly compact operators on locally convex-solid Riesz spaces.
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Temel Bulgular & Veri:We study the class of order weakly compact operators on locally solid Riesz spaces and the introduced class of generalized $b$-weakly compact operators on locally convex-solid Riesz spaces.
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Sonuç & Katkı:We prove as a consequence that some well-known results on $b$-weakly compact operators on a Banach lattice extend in an improved version to generalized $b$-weakly compact operators on a Fréchet lattice.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:b-order bounded set · order weakly compact operator · b-weakly compact operator

Abstract

We study the class of order weakly compact operators on locally solid Riesz spaces and the introduced class of generalized $b$-weakly compact operators on locally convex-solid Riesz spaces. We prove as a consequence that some well-known results on $b$-weakly compact operators on a Banach lattice extend in an improved version to generalized $b$-weakly compact operators on a Fréchet lattice.

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Bu Makaleye Atıf Yap

MACHRAFI, N., ALTIN, B. (2022). A note on topologically b-order bounded sets and generalized b-weakly compact operators. Hacettepe Journal of Mathematics and Statistics, Cilt: 51 - Sayı: 2, 483–493. https://ajindex.com/articles/669223

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Kaynakça (10)

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  2. C.D. Aliprantis and O. Burkinshaw, Locally Solid Riesz Spaces with Applications to Economics, Mathematical Surveys and Monographs 105, USA, Amer. Math. Soc., 2003
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  8. Z. Ercan, Interval-Bounded Operators and Order-Weakly Compact Operators of Riesz Spaces, Demonstr. Math. XXXI (4), 805-812, 1998
  9. G. Köthe, Topological Vector Spaces I, Springer-Verlag New York Inc., 1969
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