Please I need the solution in paper Consider a linear functional T: C[0, 1] → C, defined for every fe C[0, 1] by T(f) = ƒ(1).Show that T is continuous in C[0, 1] with respect to the supremum norm||f||==sup f(t)\.te [0,1]

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Answered: Consider a linear functional T: C[0, 1]…

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.2: Linear Independence, Basis, And Dimension

Problem 10EQ

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Consider a linear functional T: C[0, 1] → C, defined for every fe C[0, 1] by T(f) = f(1). Show that T is continuous in C[0, 1] with respect to the supremum norm ||f|| sup f(t)\. te [0,1]