On almost 2-normed vector lattices

Year 2018, Volume: 47 Issue: 5, 1094 - 1101, 16.10.2018

Bahri Turan Fatma Bilici

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.

Keywords

Normed vector lattice, n-normed space, almost 2-normed vector lattice, almost 2-Banach lattice

References

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