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Strict convexity of absolute norms on and direct sums of banach spaces

Keywords: Absolute norm , Convex function , Strict convexity , Direct sum of Banach spaces

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Abstract:

We show that an absolute normalized norm on is strictly convex if and only if the corresponding convex function on is strictly convex. In this context the monotonicity property of these norms is discussed. We also introduce the notion of the direct sum of Banach spaces and equipped with the associated norm with and characterize the strict convexity of .

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