| Title:
|
The dual of the space of functions of bounded variation (English) |
| Author:
|
Aye, Khaing Khaing |
| Author:
|
Lee, Peng Yee |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
131 |
| Issue:
|
1 |
| Year:
|
2006 |
| Pages:
|
1-9 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In the paper, we show that the space of functions of bounded variation and the space of regulated functions are, in some sense, the dual space of each other, involving the Henstock-Kurzweil-Stieltjes integral. (English) |
| Keyword:
|
bounded variation |
| Keyword:
|
two-norm space |
| Keyword:
|
dual space |
| Keyword:
|
linear functional |
| Keyword:
|
Henstock integral |
| Keyword:
|
Stieltjes integral |
| Keyword:
|
regulated function |
| MSC:
|
26A39 |
| MSC:
|
26A42 |
| MSC:
|
26A45 |
| MSC:
|
46B26 |
| MSC:
|
46E99 |
| idZBL:
|
Zbl 1112.26008 |
| idMR:
|
MR2210998 |
| DOI:
|
10.21136/MB.2006.134078 |
| . |
| Date available:
|
2009-09-24T22:23:26Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134078 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
[3] K. K. Aye: The duals of some Banach spaces.Ph.D Thesis, Nanyang Technological University, 2002. |
| Reference:
|
[4] M. Tvrdý: Linear bounded functionals on the space of regular regulated functions.Tatra Mt. Math. Publ. 8 (1996), 203–210. MR 1475282 |
| Reference:
|
[5] P. Habala, P. Hájek, V. Zizler: Introduction to Banach Spaces.1996. |
| Reference:
|
[6] P. Y. Lee: Lanzhou Lectures on Henstock Integration.World Scientific, 1989. Zbl 0699.26004, MR 1050957 |
| Reference:
|
[7] P. Y. Lee, R. Výborný: The Integral: An Easy Approach after Kurzweil and Henstock.Cambridge University Press, 2000. MR 1756319 |
| Reference:
|
[8] T. H. Hildebrandt: Introduction of the Theory of Integration.Academic Press, 1963. MR 0154957 |
| Reference:
|
[9] T. H. Hildebrandt: Linear continuous functionals on the space (BV) with weak topologies.Proc. Amer. Math. Soc. 17 (1966), 658–664. Zbl 0152.13604, MR 0193490 |
| Reference:
|
[10] Tom M. Apostol: Mathematical Analysis.1957. |
| Reference:
|
[11] W. Orlicz: Linear Functional Analysis.World Scientific, 1992. Zbl 0799.46002, MR 1182560 |
| Reference:
|
[12] K. K. Aye, P. Y. Lee: Orthogonally additive functionals on BV.Math. Bohem. 129 (2004), 411–419. MR 2102614 |
| Reference:
|
[13] Š. Schwabik: A survey of some new results for regulated functions.Seminario Brasileiro de analise 28 (1988). |
| Reference:
|
[14] M. Brokate, P. Krejčí: Duality in the space of regulated functions and the play operator.Math. Z. 245 (2003), 667–668. MR 2020705, 10.1007/s00209-003-0563-6 |
| . |
