Differential Equations and Control Processes
(Differencialnie Uravnenia i Protsesy Upravlenia)

On the Strong Uniqueness of Some Projections with Unit Norm

Author(s):

Oleg Mikhailovich Martynov

PhD in phisics and mathematics
Assoc.Professor
Dept. № 13
Zhukov Air and Space Defense Academy
Zhigarev Str., 50,
Tver, 170100, Russia

olegmartynov@yandex.ru

Abstract:

In this paper we consider some minimal projections of a space of dimension 2n onto a subspace of codimension two. It is shown that there are two types of such projections - that have the norm equal one and the projections having the norm greater than one. In both cases relative projection constants are found. For projections with unit norm, an upper estimation of the strong uniqueness constant is obtained, and it is proved that this estimation is accurate.

Keywords

• constants of strong unicity
• projection
• space
• subspace
• the relative projection constant

References:

1. Blatter J., Cheney E. W., Minimal projections on hyperplanes in sequence spaces. Ann. math. pura et appl., 101 (1974), p. 215-227
2. Walsh J. L. A closed set of normal orthogonal functions // Amer. J. Math., 45, 1923, P. 5-24
3. Lokot’ V., Martynov O. Operatory proektirovaniya v konechnomernyx prostranstvah. - Saarbrü cken: LAMBERT Academic Publishing, 2016. - 245 с

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