Conditions Which Imply a Banach Algebra is Finite Dimensional
摘要
It is a long standing conjecture that every contractible Banach algebra is finite dimensional. Motivated by this problem, we provide a survey of results in which certain conditions force a Banach algebra to be finite dimensional, with shorter proofs for a couple of them. These conditions are collected in three main groups: algebraic conditions, bounded cohomology contions and functional analytic ones.