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T-Orthogonality and Nonlinear Functionals on Topological Vector Spaces

Published online by Cambridge University Press:  20 November 2018

K. Sundaresan  and
O. P. Kapoor
K. Sundaresan
Affiliation:
University of Pittsburgh, Pittsburgh, Pennsylvania
O. P. Kapoor
Affiliation:
University of Pittsburgh, Pittsburgh, Pennsylvania
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In recent years the problem of concretely representing a class of nonlinear functionals on Banach spaces has received considerable attention. Suppose B is a Banach space equipped with an orthogonality relation ⊥ ⊂ B X B.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 25 , Issue 6 , December 1973 , pp. 1121 - 1131
Copyright
Copyright © Canadian Mathematical Society 1973

References

1. Drewnowski, L. and Orlicz, W., On representation of orthogonally additive Junctionals, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 17 (1969), 647–653.Google Scholar
2. Mizel, V. and Sundaresan, K., Representation of vector-valued nonlinear junctions, Trans. Amer. Math. Soc. 159 (1971), 11–27.Google Scholar
3. Pinsker, A. G., Sur une functionelle dans l-espace de Hilbert, Comptes Rendus (Doklady) de l'Académie des Sciences de l'USSR. XX (1938), 411–414.Google Scholar
4. Friedman, N. and Katz, M., A representation theorem for additive Junctionals, Arch. Rational Mech. Anal. 21 (1966), 49–57.Google Scholar
5. Koshi, S., On additive junctionals of measurable junction spaces, Math. J. Okayama Univ. 13 (1968), 119–127.Google Scholar
6. Dugundji, J., Topology (Allyn and Bacon, New York, 1966).Google Scholar
7. Sundaresan, K., Orthogonality and nonlinear functionals on Banach spaces, Proc. Amer. Math. Soc. 34 (1972), 187–190.Google Scholar
8. Sundaresan, K. and Woyczynski, W. A., L-orthogonally scattered measures, Pacific J. Math. 43 (1972), 785–797.Google Scholar