Banach space generated by upper Darboux integral (in Russian)

Author
K. Zheltukhin
Faculty of Mechanics and Mathematics, V. N. Karazin Kharkiv National University, 4 Svobody Sq., Kharkiv 310077, Ukraine
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.
Keywords
Banach space, bounded functions, upper Darboux integral, completion, non-isomorphic, classical Banach spaces
DOI
doi:10.30970/ms.8.2.221-226
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
Volume
8
Issue
2
Year
1997
Journal
Matematychni Studii
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