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Total convexity for powers of the norm in uniformly convex Banach spaces. (English) Zbl 0971.46005
Summary: The aim of the paper is to show that, in uniformly convex Banach spaces, the powers of the norm with exponent \(r > 1\) share a property called total convexity. Using this fact we establish a formula for determining Bergman projections on closed hyperplanes and half spaces. This leads to a method for solving linear operator equations (e.g., first order Fredholm and Volterra equations) in spaces which are uniformly convex and smooth.

46B20 Geometry and structure of normed linear spaces
47A50 Equations and inequalities involving linear operators, with vector unknowns
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