A Note on 2-Normed Grand Sequence Spaces
Öz
In this paper, we define 2-normed grand sequence space by inspiration of (Gunawan, 2001) and (Rafeiro et. al., 2018). Also, we give some basic properties of these spaces.
Anahtar Kelimeler
Grand sequence space, 2-normed space, Lebesgue sequence space.
Kaynakça
- Duyar, C., Kanber, O. and Sağır, B., (2016). On n-normed Cesaro sequence space Cesn,p. Int. Electron. J. Pure Appl. Math., 10(2): 151-159.
- Duyar, C., Sağır, B. and Oğur, O., (2017). On a class of n-normed double sequences related to p-summable double sequence space l_p^((2)). E. J. Mathematical Anal. App., 5(1): 106-111.
- Gahler, S., (1964). Lineare 2-normierte Raume, Math. Nachr., 28: 1-43.
- Gunawan, H., (2001). The space of p-summable sequences and its natural n-norm. Bull. Austral. Math. Soc., 64, 137-147.
- Iwaniec, T. and Sbordone, C., (1992). On the integrability of the Jacobian under minimal hypotheses, Arch. Ration. Mech. Anal., 119(2), 129-143.
- Jain, P. and Kumari, S., 2010. On grand Lorentz spaces and the maximal operator, Math. Student, 79.
- Oğur, O., (2018). Superposition operator on some 2-normed sequence spaces. Karaelmas Science and Engineering journal, 8(1), 288-291.
- Oğur, O., (2020). Grand Lorentz sequence space and its multiplication operator. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics , 69 (1) , 771-781.
- Rafeiro, H., Samko, S. and Umarkhadzhiev, S., (2018). Grand Lebesgue sequence spaces. Georgian Math. J., 19(2), 235-246.
- Samko, S. and Umarkhadzhiev, S., (2017), On grand Lebesgue spaces on sets of infinite measure, Math. Nachr., 290, 913-919.
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