×

Finite co-dimensional Banach spaces and some bounded recovery problems. (English) Zbl 1060.46010

The authors study the relation between the norm of a projection onto a subspace and the norm of the projection onto the complementary subspace, assuming that one of them is finite-codimensional. The results are nice, and the problem is related in some way to the problem of minimal projections. The authors, unfortunately, fail to refer to the work of Franchetti and Cheney, and to the work of Lewicky on minimal projection.

MSC:

46B20 Geometry and structure of normed linear spaces
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Dunford, D.; Schwartz, J. T., Linear Operators, Part I: General Theory (1958), INC: INC New York · Zbl 0084.10402
[2] Garling, D. J.H.; Gordon, Y., Relations between constants associated with finite dimensional Banach spaces, Israel J. Math., 9, 346-361 (1971) · Zbl 0212.14203
[3] Gordon, Y., On the projection and Macphail’s constants of \(l_p^{n\) · Zbl 0182.45202
[4] Grunbaum, B., Projection constants, Trans. Am. Soc., 95, 451-465 (1960) · Zbl 0095.09002
[5] Konig, H.; Tomczak-jaegermann, N., Norms of minimal projections, J. Funct. Anal., 119, 253-280 (1994) · Zbl 0818.46015
[6] H. Konig, C. Schutt, N. Tomczak-jaegermann, Projection constants of symmetric spaces and variant of Khintchine‘s inequality, Lecture Notes, 1999; H. Konig, C. Schutt, N. Tomczak-jaegermann, Projection constants of symmetric spaces and variant of Khintchine‘s inequality, Lecture Notes, 1999
[7] Rutovitz, D., Some parameters associated with finite dimensional Banach spaces, J. London Math. Soc., 40, 241-255 (1965) · Zbl 0125.06402
[8] Shekhtman, B., Obstacles to bounded recovery, Abstr. Appl. Anal., 6, 7, 381-400 (2001) · Zbl 1098.46014
[9] El-Shobaky, E. M.; Ali, S. M.; Takahashi, W., On the projection constants of some topological spaces and some applications, Abstr. Appl. Anal., 6, 5, 299-308 (2001) · Zbl 1021.46018
[10] El-Shobaky, E. M.; Ali, S. M.; Takahashi, W., On the projection constant problems and the existence of the metric projections in normed spaces, Abstr. Appl. Anal., 6, 7, 401-410 (2001) · Zbl 1060.41025
[11] Takahashi, W., Nonlinear functional analysis, Fixed Point Theory and Its Applications (2000), Yokohama Publishers · Zbl 0997.47002
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.