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- Nest_algebra abstract "In functional analysis, a branch of mathematics, nest algebras are a class of operator algebras that generalise the upper-triangular matrix algebras to a Hilbert space context. They were introduced by Ringrose (1965) and have many interesting properties. They are non-selfadjoint algebras, are closed in the weak operator topology and are reflexive.Nest algebras are among the simplest examples of commutative subspace lattice algebras. Indeed, they are formally defined as the algebra of bounded operators leaving invariant each subspace contained in a subspace nest, that is, a set of subspaces which is totally ordered by inclusion and is also a complete lattice. Since the orthogonal projections corresponding to the subspaces in a nest commute, nests are commutative subspace lattices.By way of an example, let us apply this definition to recover the finite-dimensional upper-triangular matrices. Let us work in the -dimensional complex vector space , and let be the standard basis. For , let be the -dimensional subspace of spanned by the first basis vectors . Letthen N is a subspace nest, and the corresponding nest algebra of n × n complex matrices M leaving each subspace in N invariant that is, satisfying for each S in N – is precisely the set of upper-triangular matrices.If we omit one or more of the subspaces Sj from N then the corresponding nest algebra consists of block upper-triangular matrices.".
- Nest_algebra wikiPageID "460461".
- Nest_algebra wikiPageRevisionID "525575794".
- Nest_algebra hasPhotoCollection Nest_algebra.
- Nest_algebra subject Category:Operator_algebras.
- Nest_algebra subject Category:Operator_theory.
- Nest_algebra type Abstraction100002137.
- Nest_algebra type Algebra106012726.
- Nest_algebra type Cognition100023271.
- Nest_algebra type Content105809192.
- Nest_algebra type Discipline105996646.
- Nest_algebra type KnowledgeDomain105999266.
- Nest_algebra type Mathematics106000644.
- Nest_algebra type OperatorAlgebras.
- Nest_algebra type PsychologicalFeature100023100.
- Nest_algebra type PureMathematics106003682.
- Nest_algebra type Science105999797.
- Nest_algebra comment "In functional analysis, a branch of mathematics, nest algebras are a class of operator algebras that generalise the upper-triangular matrix algebras to a Hilbert space context. They were introduced by Ringrose (1965) and have many interesting properties. They are non-selfadjoint algebras, are closed in the weak operator topology and are reflexive.Nest algebras are among the simplest examples of commutative subspace lattice algebras.".
- Nest_algebra label "Nest algebra".
- Nest_algebra sameAs m.02c7p0.
- Nest_algebra sameAs Q6997759.
- Nest_algebra sameAs Q6997759.
- Nest_algebra sameAs Nest_algebra.
- Nest_algebra wasDerivedFrom Nest_algebra?oldid=525575794.
- Nest_algebra isPrimaryTopicOf Nest_algebra.