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Approximate identity


In mathematics, particularly in functional analysis and ring theory, an approximate identity is a net in a Banach algebra or ring (generally without an identity) that acts as a substitute for an identity element.

A right approximate identity in a Banach algebra A is a net such that for every element a of A, Similarly, a left approximate identity in a Banach algebra A is a net such that for every element a of A, An approximate identity is a net which is both a right approximate identity and a left approximate identity.


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