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RELATIONS BETWEEN TWO CLASSES OF FUNCTIONS | ||
| Journal of Mahani Mathematical Research | ||
| دوره 10، شماره 1، مرداد 2021، صفحه 103-110 اصل مقاله (470.13 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22103/jmmrc.2021.14614.1100 | ||
| نویسنده | ||
| Javad Fathi Mourjani* | ||
| Department of Mathematics, University of hormozgan, Bandarabbas, Iran | ||
| چکیده | ||
| Let F denote a specific space of the class of was costructed by H. Khodabakhshian as a classes of separable Banach function spaces analogous to the james function spaces. In this notes we prove that l_p(α) is isomorphic to a complemented subspace of F_{α,p} and for p = 2, F_{α,p} is a closed subspace of the Waterman-Shiba space αBV^ (p) Assume F denotes a specific space of the class of F_{α,p} that was costructed by H. Khodabakhshian[2] as a classes of separable Banach function spaces analogous to the James function spaces. In this notes we prove that l_p(α) is isomorphic to a complemented subspace of F_{α,p} and for p = 2, F_{α,p} is a closed subspace of Waterman-Shiba space αBV^(p). | ||
| کلیدواژهها | ||
| Banach space؛ Complemented subspace؛ Generalized bounded variation | ||
| مراجع | ||
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[1] S. Buechler, Ph.D. Thesis, University of Texas at Austin, 1994. [2] H. Khodabakhshian, Ph.D. Thesis, University of Sistan and Baluchestan, 2008. [3] P. Azimi, J. Hagler, Example of hereditarily l1 Banach spaces failing the Scher property, Paci c J. Math. 122 (1986), 287-297. [4] M. M. Day, Normal Linear Spaces, Springer Verlag, Berlin, 1958. [5] J. Lindenstrauss and L. Tzafriri, Classical Banach Spaces, Vol.I sequences spaces, Springer Verlag, Berlin. 1996. [6] M. Shiba, On the absolute convergence of Fourier series of functions of class BV (p), Sci. Rep. Fukushima Univ. 30 (1980), 7-10. [7] D. Waterman, On convergence of Fourier series of functions of bounded generalized variation, Studia Math. 44 (1972), 107-117. [8] D. Waterman, On -bounded variation, Studia Math. 57 (1976), 33-45. | ||
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