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Introduce Banach Algebras and give some commentary and proofs over how it relates to the spectrum, resolvent sets along with the relationship to eigenvectors and eigenvalues.

Description

Introduce Banach Algebras and give some commentary and proofs over how it relates to the spectrum, resolvent sets along with the relationship to eigenvectors and eigenvalues.

Then introduce C* algebras and also give proofs, details and commentary over how it relates to spectral theory