Ranges of Bimodule Projections and Conditional Expectations
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| Title: | Ranges of Bimodule Projections and Conditional Expectations |
|---|---|
| Description: | The algebraic theory of corner subrings introduced by Lam (as an abstraction of the properties of Peirce corners eRe of a ring R associated with an idempotent e in R) is investigated here in the context of Banach and C•-algebras. We propose a general algebraic approach which includes the notion of ranges of (completely) contractive conditional expectations on C•-algebras and on ternary rings of operators, and we investigate when topological properties are consequences of the algebraic assumptions. For commutative C•-algebras we show that dense corners cannot be proper and that self-adjoint corners must be closed and always have closed complements (and may also have non-closed complements). For C•-algebras we show that Peirce corners and some more general corners are similar to self-adjoint corners. We show uniqueness of complements for certain classes of corners in general C•-algebras, and establish that a primitive C•-algebra must be prime if it has a prime Peirce corner. Further we consider corners in ternary rings of operators (TROs) and characterise corners of Hilbertian TROs as closed subspaces. |
| Authors: | Robert Pluta, Author |
| Resource Type: | eBook. |
| Subjects: | Rings (Algebra), Algebra |
| Categories: | MATHEMATICS / Algebra / Intermediate |
| Database: | eBook Collection (EBSCOhost) |
| FullText | Links: – Type: ebook-pdf Text: Availability: 0 |
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| Header | DbId: nlebk DbLabel: eBook Collection (EBSCOhost) An: 860104 RelevancyScore: 1051 AccessLevel: 6 PubType: eBook PubTypeId: ebook PreciseRelevancyScore: 1050.81640625 |
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| Items | – Name: Title Label: Title Group: Ti Data: Ranges of Bimodule Projections and Conditional Expectations – Name: Abstract Label: Description Group: Ab Data: The algebraic theory of corner subrings introduced by Lam (as an abstraction of the properties of Peirce corners eRe of a ring R associated with an idempotent e in R) is investigated here in the context of Banach and C•-algebras. We propose a general algebraic approach which includes the notion of ranges of (completely) contractive conditional expectations on C•-algebras and on ternary rings of operators, and we investigate when topological properties are consequences of the algebraic assumptions. For commutative C•-algebras we show that dense corners cannot be proper and that self-adjoint corners must be closed and always have closed complements (and may also have non-closed complements). For C•-algebras we show that Peirce corners and some more general corners are similar to self-adjoint corners. We show uniqueness of complements for certain classes of corners in general C•-algebras, and establish that a primitive C•-algebra must be prime if it has a prime Peirce corner. Further we consider corners in ternary rings of operators (TROs) and characterise corners of Hilbertian TROs as closed subspaces. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Robert+Pluta%2C+Author%22">Robert Pluta, Author</searchLink> – Name: TypePub Label: Resource Type Group: TypPub Data: eBook. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Rings+%28Algebra%29%22">Rings (Algebra)</searchLink><br /><searchLink fieldCode="DE" term="%22Algebra%22">Algebra</searchLink> – Name: SubjectBISAC Label: Categories Group: Su Data: <searchLink fieldCode="ZK" term="%22MATHEMATICS+%2F+Algebra+%2F+Intermediate%22">MATHEMATICS / Algebra / Intermediate</searchLink> |
| PLink | https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=nlebk&AN=860104 |
| RecordInfo | BibRecord: BibEntity: Classifications: – Code: 512 Scheme: ddc Type: prePub – Code: 512.25 Scheme: ddc Type: prePub Languages: – Code: eng Text: English Subjects: – SubjectFull: Rings (Algebra) Type: general – SubjectFull: Algebra Type: general Titles: – TitleFull: Ranges of Bimodule Projections and Conditional Expectations Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Robert Pluta, Author – PersonEntity: Name: NameFull: Robert Pluta, Author IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 01 Type: published Y: 2013 – D: 06 M: 07 Type: profile Y: 2017 Identifiers: – Type: isbn-print Value: 9781443846127 – Type: isbn-electronic Value: 9781443867863 Titles: – TitleFull: Ranges of Bimodule Projections and Conditional Expectations Type: main |
| ResultId | 1 |
