Abstract
A Banach algebra is an associative algebra A with a norm ∥ ⋅ ∥ such that A is a Banach space in this norm, and the norm satisfies ∥ xy ∥ ≤ ∥ x ∥ ∥ y ∥ on all products xy of elements x, y ∈ A. Two examples of Banach algebras encountered to this point are: (i) C(X), the algebra of continuous functions on a compact Hausdorff space X, and (ii) B(V ), the algebra of all bounded linear operators acting on V.
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