Let H = (2 be equipped with the inner product (x, y) = E-1 "kYk• LetT : H → H be defined bySo(Tx)kif k = 1.%3D||Xk-1 if k > 2.(i) Prove that ơp(T) = Ø.(ii) Prove that 10 € p(T).

Given H=l2 is equipped with the inner product x,y=∑k=1∞xkyk and T:H→H be defined by Txk=0 ,…

Answered: (2 be equipped with the inner product…

(2 be equipped with the inner product (x, y) = XkYk: Let T : H → H be defined by |0 (Tx)k : if k = 1. Tk-1 if k 2 2. (i) Prove that op(T) = (). (ii) Prove that 10 € p(T).

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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Question

Let H = (2 be equipped with the inner product (x, y) = E-1 "kYk• Let
T : H → H be defined by
So
(Tx)k
if k = 1.
%3D
||
Xk-1 if k > 2.
(i) Prove that ơp(T) = Ø.
(ii) Prove that 10 € p(T).

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