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http://dx.doi.org/10.4134/JKMS.2004.41.1.157

PLANK PROBLEMS, POLARIZATION AND CHEBYSHEV CONSTANTS  

Revesz, Szilard-Gy. (A. Renyi Institute of Mathematics Hungarian Academy of Sciences Budapest)
Sarantopoulos, Yannis (National Technical University School of Applied Mathematical and Physical Sciences Department of Mathematics)
Publication Information
Journal of the Korean Mathematical Society / v.41, no.1, 2004 , pp. 157-174 More about this Journal
Abstract
In this work we discuss "plank problems" for complex Banach spaces and in particular for the classical $L^{p}(\mu)$ spaces. In the case $1\;{\leq}\;p\;{\leq}\;2$ we obtain optimal results and for finite dimensional complex Banach spaces, in a special case, we have improved an early result by K. Ball [3]. By using these results, in some cases we are able to find best possible lower bounds for the norms of homogeneous polynomials which are products of linear forms. In particular, we give an estimate in the case of a real Hilbert space which seems to be a difficult problem. We have also obtained some results on the so-called n-th (linear) polarization constant of a Banach space which is an isometric property of the space. Finally, known polynomial inequalities have been derived as simple consequences of various results related to plank problems.
Keywords
Plank problem; homogeneous polynomials over normed spaces; linear polarization constants; quasi-monotonous sequences; Banach-Mazur distance; characterization of Banach spaces; local theory of Banach spaces; com-plexification of Banach spaces; weak-star convergent subsequences;
Citations & Related Records

Times Cited By Web Of Science : 14  (Related Records In Web of Science)
Times Cited By SCOPUS : 17
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