The operator of minimal continuance of linear functionals
- 29 Downloads
In terms of weak differentiability of norms and algebraic complementation of subspaces, the single-valuedness of the Hahn-Banach continuation is characterized, as well as its linearity as an operator. The connection is established between this continuation and the best approximation by the annihilator of the given subspace.
KeywordsLinear Functional Minimal Continuance Algebraic Complementation Weak Differentiability
Unable to display preview. Download preview PDF.
- 1.N. I. Akhiezer and M. G. Krein, On Some Questions in Moment Theory [in Russian], Kharkov Univ. Press, Kharkov (1938).Google Scholar
- 2.A. L. Garkavi, “On uniqueness of solution ofL-problems of moments,” Izv. Akad. Nauk, SSSR, Ser. Mat.,28, No. 3, 553–570 (1964).Google Scholar
- 3.E. T. Poulsen, “Eindeutige Hahn-Banach Erweiterung,” Math. Ann.,”162, No. 2, 225–227 (1966).Google Scholar
- 4.N. Dunford and J. J. Schwartz, Linear Operators, Vol. 1, Interscience, New York (1958).Google Scholar
- 5.R. R. Phelps, “Uniqueness of Hahn-Banach extensions and unique best approximation,” Trans. Am. Math. Soc.,95, No. 2, 238–255 (1960).Google Scholar
- 6.I. Singer, Best Approximation in Normed Linear Spaces by Elements of Linear Subspaces, Springer-Verlag, New York (1970).Google Scholar
- 7.A. L. Garkavi, “On the best approximation by elements of infinite-dimensional subspaces of one class,” Mat. Sb.,62, No. 1, 104–120 (1963).Google Scholar
- 8.P. K. Belobrov, “On Chebyshev points of systems of shifts of subspaces in Banach space,” Mat. Zametki,8, No. 1, 29–40 (1970).Google Scholar
- 9.M. M. Day, Normed Linear Spaces, Academic Press, New York (1962).Google Scholar