Answered: Let H be a Hilbert space and letR, S, T…

Let H be a Hilbert space and letR, S, T : H → H be bounded linear operators. Suppose that S is compact. Show thatR ◦ S ◦ T is compact.

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 be a Hilbert space and let
R, S, T : H → H be bounded linear operators. Suppose that S is compact. Show that
R ◦ S ◦ T is compact.

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