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Functional Analysis Exercises 12 : Linear Operators

Avishek Sen Gupta on 19 October 2022

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:

\[\blacksquare\]

tags: Mathematics - Proof - Functional Analysis - Pure Mathematics - Kreyszig