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- Approximate_identity abstract "In functional analysis and ring theory, an approximate identity is a net in a Banach algebra or ring (possibly without an identity) that acts as a substitute for an identity element.More precisely, a right approximate identity in a Banach algebra, A, is a net (or a sequence) such that for every element, a, of A, the net (or sequence)has limit a.Similarly, a left approximate identity is a netsuch that for every element, a, of A, the net (or sequence)has limit a.An approximate identity is a right approximate identity which is also a left approximate identity.For C*-algebras, a right (or left) approximate identity is the same as an approximate identity. Every C*-algebra has an approximate identity of positive elements of norm ≤ 1; indeed, the net of all positive elements of norm ≤ 1; in A with its natural order always suffices. This is called the canonical approximate identity of a C*-algebra. Approximate identities of C*-algebras are not unique. For example, for compact operators acting on a Hilbert space, the net consisting of finite rank projections would be another approximate identity.An approximate identity in a convolution algebra plays the same role as a sequence of function approximations to the Dirac delta function (which is the identity element for convolution). For example the Fejér kernels of Fourier series theory give rise to an approximate identity.".
- Approximate_identity wikiPageID "949628".
- Approximate_identity wikiPageRevisionID "543505260".
- Approximate_identity hasPhotoCollection Approximate_identity.
- Approximate_identity subject Category:Banach_algebras.
- Approximate_identity type Abstraction100002137.
- Approximate_identity type Algebra106012726.
- Approximate_identity type BanachAlgebras.
- Approximate_identity type Cognition100023271.
- Approximate_identity type Content105809192.
- Approximate_identity type Discipline105996646.
- Approximate_identity type KnowledgeDomain105999266.
- Approximate_identity type Mathematics106000644.
- Approximate_identity type PsychologicalFeature100023100.
- Approximate_identity type PureMathematics106003682.
- Approximate_identity type Science105999797.
- Approximate_identity comment "In functional analysis and ring theory, an approximate identity is a net in a Banach algebra or ring (possibly without an identity) that acts as a substitute for an identity element.More precisely, a right approximate identity in a Banach algebra, A, is a net (or a sequence) such that for every element, a, of A, the net (or sequence)has limit a.Similarly, a left approximate identity is a netsuch that for every element, a, of A, the net (or sequence)has limit a.An approximate identity is a right approximate identity which is also a left approximate identity.For C*-algebras, a right (or left) approximate identity is the same as an approximate identity. ".
- Approximate_identity label "Approximate identity".
- Approximate_identity label "Approximation de l'unité".
- Approximate_identity label "Approximation der Eins".
- Approximate_identity sameAs Approximation_der_Eins.
- Approximate_identity sameAs Approximation_de_l'unité.
- Approximate_identity sameAs m.03smpl.
- Approximate_identity sameAs Q621743.
- Approximate_identity sameAs Q621743.
- Approximate_identity sameAs Approximate_identity.
- Approximate_identity wasDerivedFrom Approximate_identity?oldid=543505260.
- Approximate_identity isPrimaryTopicOf Approximate_identity.