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Conditions for uniqueness of a projector with unit norm
V. P. Odinets Leningrad Finance and Economics Institute
Abstract:
Suppose that in a normed linear space $B$ there exists a projector with unit norm onto a subspace $D$. A sufficient condition for this projector to be unique is the existence of a set $M\subset D^*$ which is total on $D$, each functional in which attains its norm on the unit sphere in $D$ and has a unique extension onto $B$ with preservation of norm. As corollaries to this fact, we obtain a series of sufficient conditions for uniqueness (some of which were previously known) as well as a necessary and sufficient condition for uniqueness.
Received: 17.10.1974
Citation:
V. P. Odinets, “Conditions for uniqueness of a projector with unit norm”, Mat. Zametki, 22:1 (1977), 45–49; Math. Notes, 22:1 (1977), 515–517
Linking options:
https://www.mathnet.ru/eng/mzm8023 https://www.mathnet.ru/eng/mzm/v22/i1/p45
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Statistics & downloads: |
Abstract page: | 199 | Full-text PDF : | 70 | First page: | 1 |
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