Banach algebra cohomology is a branch of functional analysis and abstract algebra that studies Banach algebras using the techniques of cohomology. It provides a way to investigate the structure of Banach algebras and their representations through the lens of cohomological methods, which originated in algebraic topology. ### Basic Concepts: 1. **Banach Algebras**: A Banach algebra \( A \) is a complete normed algebra over the field of complex or real numbers.
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