Multiplier algebra

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In operator algebras, every C*-algebra A is associated with an unital C*-algebra called its multiplier algebra, denoted by M(A). It is the noncommutative analog of Stone–Čech compactification. When A is non-unital, M(A) is the largest unital C*-algebra that contains A as an ideal in a "non-degenerate" way. When A is unital, one has A = M(A).

For example, if A is the C*-algebra of compact operators acting on a Hilbert space, M(A) is the C*-algebra of all bounded operators on H.