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Topological Algebras of Bounded Operators with Locally Solid Riesz Spaces

Yıl 2018, Cilt: 11 Sayı: 3, 543 - 549, 30.12.2018
https://doi.org/10.18185/erzifbed.413678

Öz

Suppose  is a vector lattice
and  is a locally solid
vector lattice. An operator  is said to be -bounded if, for every order bounded set   is topological bounded
in . In this paper, we study on algebraic properties of -bounded operators with the equicontinuous convergence
topology and uniform convergence topology
.

Kaynakça

  • Aliprantis, C.D., Burkinshaw, O. 2003. Locally Solid Riesz Spaces with Applications to Economics 2nd ed., American Mathematical Society, United States.
  • Aliprantis, C.D., Burkinshaw, O. 2006. Positive Operators, Springer Netherlands, London.
  • Aydın, A., Gorokhova S.G., Gül, H. 2018. Nonstandard Hulls of Lattice-Normed Ordered Vector Spaces, Turkish Journal of Mathematics, 42(1), 155 – 163.
  • Aydın, A., Emel'yanov E., Erkurşun N.Ö., Marabeh, M.A.A. 2018. Compact-Like Operators in Lattice-Normed Spaces, Indagationes Mathematicae, 29(1), 633-656.
  • Hong, L. 2016. On Order Bounded Subsets of Locally Solid Riesz Spaces, Quaestiones Mathematicae, 39(3), 381-389.
  • Troitsky, V.G. 2004. Measures of Non-Compactness of Operators on Banach Lattices, Positivity, 8(2), 165–178.
  • Zabeti, O. 2017. Topological Algebras of Locally Solid Vector Subspaces of Order Bounded Operators, Positivity, 21(4), 1253–1259.

Topological Algebras of Bounded Operators with Locally Solid Riesz Spaces

Yıl 2018, Cilt: 11 Sayı: 3, 543 - 549, 30.12.2018
https://doi.org/10.18185/erzifbed.413678

Öz

bir kafes uzayı ve de bir yerel solid kafes uzayı olsun. Eğer 'deki her sıra sınırlıalt kümesi için, 'de topolojik olarak sınırlı oluyorsa;  operatörüne -sınırlı operatör denir. Bu çalışmamızda, -sınırlılığın cebirsel özelliklerini denk-süreklilik
yakınsamasındaki ve düzgün yakınsamasındaki topolojilere göre inceledik.

Kaynakça

  • Aliprantis, C.D., Burkinshaw, O. 2003. Locally Solid Riesz Spaces with Applications to Economics 2nd ed., American Mathematical Society, United States.
  • Aliprantis, C.D., Burkinshaw, O. 2006. Positive Operators, Springer Netherlands, London.
  • Aydın, A., Gorokhova S.G., Gül, H. 2018. Nonstandard Hulls of Lattice-Normed Ordered Vector Spaces, Turkish Journal of Mathematics, 42(1), 155 – 163.
  • Aydın, A., Emel'yanov E., Erkurşun N.Ö., Marabeh, M.A.A. 2018. Compact-Like Operators in Lattice-Normed Spaces, Indagationes Mathematicae, 29(1), 633-656.
  • Hong, L. 2016. On Order Bounded Subsets of Locally Solid Riesz Spaces, Quaestiones Mathematicae, 39(3), 381-389.
  • Troitsky, V.G. 2004. Measures of Non-Compactness of Operators on Banach Lattices, Positivity, 8(2), 165–178.
  • Zabeti, O. 2017. Topological Algebras of Locally Solid Vector Subspaces of Order Bounded Operators, Positivity, 21(4), 1253–1259.
Toplam 7 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Mühendislik
Bölüm Makaleler
Yazarlar

Abdullah AYDIN

Yayımlanma Tarihi 30 Aralık 2018
Yayımlandığı Sayı Yıl 2018 Cilt: 11 Sayı: 3

Kaynak Göster

APA AYDIN, A. (2018). Topological Algebras of Bounded Operators with Locally Solid Riesz Spaces. Erzincan University Journal of Science and Technology, 11(3), 543-549. https://doi.org/10.18185/erzifbed.413678