(b)Define T: (C¹ [0, 1], || · ||…) → (℃ [0, 1],|||| by Tf = f'. Show that T is notcontinuous. Is Z(T) closed? Justify.4

T:C'[0,1], .∞→C'[0,1], .∞ T(f)=f' Let f(x)=xn then T(x)=nxn-1 T(x)=nxn-1 as n→∞, T(x)→∞ So T is…

Answered: Define T: (C¹ [0, 1], || · ||…) → (℃…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Define T: (C¹ [0, 1], || · ||…) → (℃ [0, 1], || ||) by Tf = f'. Show that T is not continuous. Is Z(T) closed? Justify.