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Geometry of Banach spaces of trinomials

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Muñoz-Fernández, Gustavo A. and Seoane-Sepúlveda, Juan B. (2008) Geometry of Banach spaces of trinomials. Journal of Mathematical Analysis and Applications, 340 (2). pp. 1069-1087. ISSN 0022-247X

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Official URL: http://www.sciencedirect.com/science/article/pii/S0022247X07011237


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Abstract

For each pair of numbers m, n epsilon N with m > n, we consider the norm on R-3 given by parallel to(a, b, c)parallel to m,n = sup{vertical bar ax(m) +bx(n) +C vertical bar: x epsilon [-1, 1]} for every (a, b, c) epsilon R-3. We investigate some geometrical properties of these norms. We provide an explicit formula for parallel to center dot parallel to m,n, a full description of the extreme points of the corresponding unit balls and a parametrization and a plot of their unit spheres.


Item Type:Article
Uncontrolled Keywords:Convexity; Extreme points; Polynomial norms; Trinomials
Subjects:Sciences > Mathematics > Functional analysis and Operator theory
ID Code:17087
Deposited On:13 Nov 2012 09:50
Last Modified:25 Nov 2016 12:36

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