Hi!

I'm studying Kahane, Zelazko paper "A characterization of maximal ideals in commutative Banach algebras" and I've problem with one statement in the proof of Theorem2.

Below is this theorem and part of the proof with 'red rectangle' - how can I proof/show this estimation and implication?

Any help will be highly appreciated.

Bes regards

[2] E. C. Titchmarsh,Theory of functions, Oxford 1939.