For X and Y normed linear spaces, let {T} be a sequence in L(X, Y) such that Tn →T in L(X,Y)and let {n} be a sequence in X such that un → u in X.(a) Let ε = 1 in the definition of convergence of {T} to T in L(X, Y).||T|| ≤M, \n N, where M = sup{||T₁||, ||T₂||, ..||TN-1||, 1 + ||T||}, for some NE N.(b) for all n € N, ||Tn(Un) — T(u)||y ≤ ||Tn|| · ||Un − u||x + ||Tn − T|| · ||u|| x.Use (a) and (b) to show that Tn(un) → T(u) in Y.

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Answered: For X and Y normed linear spaces, let…

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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