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Gliding hump properties of matrix domains. (English) Zbl 1075.46003
Summary: Gliding hump properties play an important role in numerous topics in analysis, for instance, they are used as a substitute for the uniform boundedness principle. Since examples of sequence spaces having certain gliding hump properties are rare, the main aim of this paper is to present classes of infinite matrices \(A\) such that the matrix domain \(E_A\) has a certain gliding hump property whenever a given sequence space \(E\) has this property.

46A45 Sequence spaces (including Köthe sequence spaces)
40D25 Inclusion and equivalence theorems in summability theory
40H05 Functional analytic methods in summability
matrix domains
Full Text: DOI
[1] J. Boos, Classical and modern methods in summability, Oxford University Press (Oxford, 2000). · Zbl 0954.40001
[2] J. Boos and D. J. Fleming, Gliding hump properties and some applications, J. Math. Math. Sci., 18(1995), 121–132. · Zbl 0824.46007
[3] J. Boos, D.J. Fleming and T. Leiger, Sequence spaces with oscillating properties, J. Math. Anal. Appl., 200(1996), 519–537. · Zbl 0885.46006
[4] J. Boos and T. Leiger, General theorems of Mazur-Orlicz type, Studia Math., 92(1989), 1–19. · Zbl 0703.46004
[5] J. Boos and T. Leiger, The signed weak gliding hump property, Acta Comm. Univ. Tartuensis, 970(1994), 13–22. · Zbl 1210.40012
[6] P. K. Kamthan and M. Gupta, Sequence spaces and series, Marcel Dekker (New York-Basel, 1981). · Zbl 0447.46002
[7] H. Lebesgue, Sur les integrales singulieres, Ann. de Toulouse, 1(1909), 25–117. · JFM 40.0762.03
[8] Peng Yee Lee, Sequence spaces and the gliding hump property, Proceedings of the International Conference on Functional Analysis and Global Analysis (Quezon City, 1992), special issue (1993), 65–72. · Zbl 0811.46008
[9] D. Noll, Sequential completeness and spaces with the gliding humps property, Manuscripta Math., 66(1990), 237–252. · Zbl 0713.46009
[10] A. K. Snyder, Consistency theory in semiconservative spaces, Studia Math., 71(1982), 1–13. · Zbl 0524.46003
[11] C. E. Stuart, Weak sequential completeness in sequence spaces, Thesis, New Mexico State University (Las Cruces, New Mexico, 1993).
[12] C. E. Stuart, Weak sequential completeness of {\(\beta\)}-duals, Rocky Mountain J. Math., 26(1996), 1559–1568. · Zbl 0885.46007
[13] C. Swartz, Infinite matrices and the gliding hump, World Scientific Publishing (River Edge, NJ, 1996). · Zbl 0923.46003
[14] A. Wilansky, Summability through functional analysis, North Holland (Amsterdam-New York-Oxford, 1984). · Zbl 0531.40008
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