International Journal of Nonlinear Analysis and Applications
The Daniell's functional on a Banach lattice
Document Type : Research Paper
Authors
Mathematics Department, College of Science, Al-Qadisiyah University, Iraq
Abstract
In this paper, we presented both the concept of Daniell space and the extension of Daniell space with some basic results related to these spaces when the Daniell functional on a Banach lattice space. The extension of Daniell's space has been proven a complete space.
Keywords
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[2] R.B. Ash, Real analysis and probability, University of Illinois, Academics Press, 1972.
[3] R.B. Ash, Real analysis and probability, Academics Press, New York, 1992.
[4] J. Banasiak, Banach Lattices in Applications, University of Pretoria, Pretoria, South Africa, Available at https://www.up.ac.za/media/shared/259/Documents/Teaching%20material/ablbook.zp158048.pdf
[5] E. Blackstone and P. Mikusinski, The Daniell integral, arXiv:1401.0310v1[math.CA].
[6] G.A.M. Jeurnink, Integration of functions with Values in a Banach Lattice, Catholic university, Nijmegen, 1982.
[7] J.L. Kelley, General Topology, Van Nostrand Company Inc., 1955.
[8] S.S. Kutateladze, Nonstandard Analysis and Vector Lattices, Springer Science+Business Media Dordrecht, 2000.
[9] W.A.J. Luxemburg and A.C. Zaanen, Riesz Spaces, North-Holland Publishing Company, 1971.
[10] F.A. Noori, Measure Theory and Applications, Deposit number in the National Library and Archives in Baghdad, 1780. First edition, Iraq, 2018.
[11] A.A. Pedgaonkar, Daniell Integration for Banach Space Valued Vector Maps, Int. J. Latest Res. Sci. Technol. 4 (2015), no. 6, 21–23.
[12] R.E. Shermoen, An Introduction to General Integrals, M.S.C. thesis, the Faculty of the Oklahoma State University, 1965.
[13] D.H.Tucker and H.B. Maynard, Vector and Operator Valued Measures and Applications, University of Utah, 1973.
[14] E.M. Wadsworth, Daniell integral, Msc. thesis, University of Montana, 1965.
[15] M.R. Weber, Finite Elements in Vector Lattices, Walter de Gruyter GmbH, Berlin/Boston, 2014.
[16] A.C. Zaanem, Introduction to Operator Theory in Riesz Spaces, springer-Verlag Berlin Heidelberg, 1997.
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Volume 14, Issue 5
May 2023Pages 95-101
- Receive Date: 21 December 2022
- Revise Date: 13 February 2023
- Accept Date: 18 March 2023