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. == Definition == A right approximate identity in a Banach algebra A is a net { e λ : λ ∈ Λ } {\displaystyle \{e_{\lambda }:\lambda \in \Lambda \}} such that for every element a of A, lim λ ∈ Λ ‖ a e λ − a ‖ = 0.
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. == Definition == A right approximate identity in a Banach algebra A is a net { e λ : λ ∈ Λ } {\displaystyle \{e_{\lambda }:\lambda \in \Lambda \}} such that for every element a of A, lim λ ∈ Λ ‖ a e λ − a ‖ = 0.
Source: Wikipedia "Approximate identity" · CC BY-SA 4.0
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