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Dergiler / Turkish Journal of Mathematics / 2020 / Cilt: 44 - Sayı: 2

On orthomorphism elements in ordered algebra

Bahri TURAN
Hüma GÜRKÖK
Sayfa
403–408
Yayın Tarihi
2020-03-01
DOI
—
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Then, under the same hypotheses, it is obtained that Orthe C is an f -algebra with a unit e.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:Let C be an ordered algebra with a unit e.
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Temel Bulgular & Veri:Firstly, it is shown that if C is an ordered algebra such that Cr , the set of all regular elements of C , is a Riesz space with the principal projection property and Orthe C is topologically full with respect to Ie , then Be = Orthe C holds, where Be is the band generated by e in Cr .
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Sonuç & Katkı:Then, under the same hypotheses, it is obtained that Orthe C is an f -algebra with a unit e.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Ordered algebra · orthomorphism elements · orthomorphism

Abstract

Let C be an ordered algebra with a unit e. The class of orthomorphism elements Orthe C of C was introduced and studied by Alekhno in ”The order continuity in ordered algebras”. If C = L G , where G is a Dedekind complete Riesz space, this class coincides with the band Orth G of all orthomorphism operators on G. In this study, the properties of orthomorphism elements similar to properties of orthomorphism operators are obtained. Firstly, it is shown that if C is an ordered algebra such that Cr , the set of all regular elements of C , is a Riesz space with the principal projection property and Orthe C is topologically full with respect to Ie , then Be = Orthe C holds, where Be is the band generated by e in Cr . Then, under the same hypotheses, it is obtained that Orthe C is an f -algebra with a unit e.

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Bu Makaleye Atıf Yap

TURAN, B., GÜRKÖK, H. (2020). On orthomorphism elements in ordered algebra. Turkish Journal of Mathematics, Cilt: 44 - Sayı: 2, 403–408. https://ajindex.com/articles/185554

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Kaynakça (6)

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  2. 21 (2): 539-574. doi: 10.1007/s11117-016- 0406-4 [2] Alekhno EA. The irreducibility in ordered Banach algebras. Positivity 2012
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  5. Schaefer HH. Banach Lattices and Positive Operators. Berlin, Germany: Springer, 1991. doi: 10.1007/978-3-642- 65970-6 [8] Turan B. On f -linearity and f -orthomorphisms. Positivity 2000
  6. Zaanen AC. Riesz Spaces II. Amsterdam, Holland: North Holland Publishing Company, 1983.