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 Mat. Zametki, 1977, Volume 22, Issue 1, Pages 45–49 (Mi mz8023)

Conditions for uniqueness of a projector with unit norm

V. P. Odinets

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.

Full text: PDF file (464 kB)

English version:
Mathematical Notes, 1977, 22:1, 515–517

Bibliographic databases:

UDC: 513.88

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

Citation in format AMSBIB
\Bibitem{Odi77} \by V.~P.~Odinets \paper Conditions for uniqueness of a~projector with unit norm \jour Mat. Zametki \yr 1977 \vol 22 \issue 1 \pages 45--49 \mathnet{http://mi.mathnet.ru/mz8023} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=454598} \zmath{https://zbmath.org/?q=an:0357.46029} \transl \jour Math. Notes \yr 1977 \vol 22 \issue 1 \pages 515--517 \crossref{https://doi.org/10.1007/BF01147691}