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Abstrakty
We show that the Banach space D(0,1) of all scalar (real or complex) functions on [0,1) that areright continuous at each point of [0,1) with left-hand limitat each point of (0,1] equipped with the uniform convergencetopology is primary.
Słowa kluczowe
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Rocznik
Tom
Strony
111--129
Opis fizyczny
Bibliogr. 16 poz.
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autor
- Faculty of Mathematics and Computer Science, Adam Mickiewicz University, michalak@amu.edu.pl
Bibliografia
- [1] D. Alspach and Y. Benyamini, Primariness of spaces of continuous functions on ordinals, Israel J. Math. 27 (1977), 64-92.
- [2] P. Billard, Sur la primarité des espaces (C(α), Studia Math. 62 (1978), 143-162.
- [3] H. H. Corson, The weak topology of a Banach space, Trans. Amer. Math. Soc. 101 (1961), 1-15.
- [4] L. Drewnowski, Continuity of monotone functions with values in Banach lattices, in book Recent Progress in Functiona Analysis. Proceedings of the International Functional Analysis Meeting on the Occasion of the 70th Birthday of Professor Manuel Valdivia, Valencia, Spain, July 3-7, 2000 Elsevier (2001), 185-199.
- [5] L. Drewnowski and J. W. Roberts, On the primariness of the Banach space \(l_\infty/c_0\), Proc. Amer. Math. Soc. 112 (1991), 949-957.
- [6] R. Engelking, General topology, Monografie Matematyczne 60, PWN - Polish Scientific Publishers, Warszawa 1977.
- [7] K. Kuratowski, Topologie I, Monografie Matematyczne 20, PWN - Polish Scientific Publishers, Warszawa 1948.
- [8] J. Lindenstrauss and A. Pełczyński, Contributions to the theory of the classical Banach spaces, J. Funct. Anal. 8 (1971), 225-249.
- [9] J. Lindenstrauss and L. Tzafriri, Classical Banach Spaces I, Springer-Verlag, Ergebnisse der Mathematik und ihrer Grenzgebite 92, Berlin, Heidelberg, New York, 1977.
- [10] A. Michalak, On monotonic functions from the unit interval into a Banach space with uncountable sets of points of discontinuity, Studia Math. 155 (2003), 171-182.
- [11] A. Michalak, On continuous linear operators on (D(0, 1)) with nonseparable ranges, Comment. Math. 43 (2003), 221-248.
- [12] I. P. Natanson, Theory of functions of a real variable, Moscow, Leningrad 1950 (Russian).
- [13] W. M. Patterson, Complemented \(c_0\)-subspaces of a nonseparable (C(K))-space, Canadian Math. Bull. 36 (1993), 351-357.
- [14] A. Pełczyński, On \(C(S)\) subspaces of separable Banach spaces, Studia Math. 31 (1968), 513-522.
- [15] H. P. Rosenthal, On factors of (C([0, 1])) with nonseparable dual, Israel J. Math. 13 (1973), 361-378.
- [16] M. Talagrand, Renormages de quelques C(K), Israel J. Math. 54 (1986), 327-334.
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Bibliografia
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bwmeta1.element.baztech-article-BUS2-0007-0044