(c) Show that T' is not bounded, and explain why this is not in contradiction with the OpenMapping Theorem and the Bounded Inverse Theorem. 3.* Let X be the space of continuous functions x : [1,∞0) → R which have compact support, that isthere exists a compact interval I, of [1, 0) such that x(t) = 0 Vt E [1,∞) \ Iy. Consider X withthe norm ||x|| = max |x(t)| and define the mapping T : X → X as1E[1,00)(Tx)(1) :x(1).for every t e [1, ∞).

Af first we will show that T is bijective and hence its inverse T -1 exists. Then we will find that…

Answered: (c) Show that T-l is not bounded, and…

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter3: Functions

Section3.3: Rates Of Change And Behavior Of Graphs

Problem 2SE: If a functionfis increasing on (a,b) and decreasing on (b,c) , then what can be said about the local...

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(c) Show that T-l is not bounded, and explain why this is not in contradiction with the Open Mapping Theorem and the Bounded Inverse Theorem.