Functional Analysis Exercises 12 : Linear Operators

Avishek Sen Gupta on 19 October 2022

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This post lists solutions to the exercises in the Bounded and Continuous Linear Operators section 2.7 of Erwin Kreyszig’s Introductory Functional Analysis with Applications. This is a work in progress, and proofs may be refined over time.

2.7.1. Prove that 1) \(\Vert T_1 T_2 \Vert \leq \Vert T_1 \Vert \Vert T_2 \Vert\) and 2) \(\Vert T^n \Vert \leq {\Vert T \Vert}^n\).

Proof:

\[\blacksquare\]

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