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Dergiler / Hacettepe Journal of Mathematics and Statistics / 2026 / Volume: 47 Issue: 5

On almost 2-normed vector lattices

Bahri Turan(GAZI UNIVERSITY, FACULTY OF SCIENCE, DEPARTMENT OF MATHEMATICS)
Fatma Bilici(GAZI UNIVERSITY, FACULTY OF SCIENCE, DEPARTMENT OF MATHEMATICS)
Sayfa
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Yayın Tarihi
2018-10-16
DOI
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

Then, some theoretical examples and results are given.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:In this paper, we discuss the transformation of a normed vector lattice definition into a 2-normed vector lattice definition and examine the definition of $n$-Banach lattice given by Sağır and Güngör in [A note on $n$-Banach lattices, J.
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Temel Bulgular & Veri:We also give definitions of an almost 2-normed vector lattice and an almost 2-Banach lattice.
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Sonuç & Katkı:Then, some theoretical examples and results are given.
🔬Tür:Research Article
📍Kapsam:2015 Verileri
⚙️Değişkenler:Normed vector lattice · n-normed space · almost 2-normed vector lattice

Abstract

In this paper, we discuss the transformation of a normed vector lattice definition into a 2-normed vector lattice definition and examine the definition of $n$-Banach lattice given by Sağır and Güngör in [A note on $n$-Banach lattices, J. Appl. Funct. Anal., 2015]. We also give definitions of an almost 2-normed vector lattice and an almost 2-Banach lattice. Then, some theoretical examples and results are given.

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Bu Makaleye Atıf Yap

Turan, B., Bilici, F. (2018). On almost 2-normed vector lattices. Hacettepe Journal of Mathematics and Statistics, Volume: 47 Issue: 5. https://ajindex.com/articles/1402879

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Kaynakça (9)

  1. Aliprantis, C.D. and Burkinshaw, O. Positive operators, Academic Press, Orlando, 1985.
  2. Gähler, S. Lineare 2-normierte räume, Math. Nachr. 28, 1-43, 1964.
  3. Gunawan, H. The space of p-summable sequences and its natural n-norms, Bull. Austral. Math. Soc. 64, 137-147, 2001.
  4. Gunawan, H. and Mashadi, M. On n-normed spaces, Int. J. Math. Math. Sci. 27, 631-639, 2001.
  5. Idris, M., Ekariani, S. and Gunawan, H. On the space of p-summable sequences, Mat. Vesnik. 65, 58-63, 2013.
  6. Luxemburg, W. A. J. and Zaanen, A. C. Riesz spaces I, North-Holland, Amsterdam, 1971.
  7. Sağır, B. and Güngör, N. A note on n-Banach lattices, J. Appl. Funct. Anal. 10, 70-77, 2015.
  8. Schaefer, H.H. Banach lattices and positive operators, Springer, Grundlehren 215, Berlin, 1974.
  9. Zaanen, A. C. Riesz spaces II, North-Holland, Amsterdam, 1983.