Exercise 3 Prove that if S and T are both bounded linear operators from the normedspace X to the normed space Y, then for all a E C and B E C the operator H defined byÂĤ = a$ + SÎa) is a linear operator.b) is a bounded operator.

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Answered: • Exercise 3 Prove that if S and T are…

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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• Exercise 3 Prove that if S and T are both bounded linear operators from the normed space X to the normed space Y, then for all a E C and BE C the operator H defined by ÎĤ = aŜ + BÎ a) is a linear operator. b) is a bounded operator.