Banach space generated by upper Darboux integral (in Russian) |
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| Author |
zheltukhina@ilt.kharkov.ua
Faculty of Mechanics and Mathematics, V. N. Karazin Kharkiv National University, 4 Svobody Sq., Kharkiv 310077, Ukraine
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| Abstract |
Banach space which is the completion of all bounded (not
necessarily measurable) functions on $[0,1]$
with norm which equals the upper Darboux integral is introduced. It is
proved that this space is not isomorphic to the~classical Banach spaces.
Some
questions of its geometry are considered.
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| Keywords |
Banach space, bounded functions, upper Darboux integral, completion, non-isomorphic, classical Banach spaces
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| DOI |
doi:10.30970/ms.8.2.221-226
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Reference |
1. Фихтенгольц Г.М. Курс дифференциального и интегрального исчиления: В 3-х т. – Т.2, М.: Наука, 1966.
2. Lindenstrauss J., Tzafriri L. Classical Banach Spaces I. – Springer-Verlag, 1977 |
| Pages |
221-226
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| Volume |
8
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| Issue |
2
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| Year |
1997
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| Journal |
Matematychni Studii
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| Full text of paper | |
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