Let X be a real normed linear space, and let K be a convex set in X, having 0 as an interior point. Let h be the support functional of K and define K° = {x* € X*: h(x*) < 1}. Now for xe X, let p(x) = sup (x, x*). Show that p is equal to the Minkowski functional of K.

Let X be a real normed linear space, and let K be a convex set in X, having 0 as an interior point. Let h be the support functional of K and define K° = {x* € X: h(x) < 1}. Now for xe X, let p(x) = sup (x, x*). Show that p is equal to the Minkowski functional of K.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.4: Linear Transformations

Problem 34EQ

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