| Description |
1 online resource (xiii, 241 pages) |
| Physical Medium |
polychrome |
| Description |
text file |
| Bibliography |
Includes bibliographical references (pages 233-235) and indexes. |
| Contents |
1. Real Banach and Hilbert spaces. 1.1. Complexification of real Banach and Hilbert spaces. 1.2. Spectral decomposition theorem in real Hilbert spaces -- 2. Real Banach algebras. 2.1. Definition and complexification. 2.2. Divisible real Banach algebras. 2.3. The topological group of invertible elements and its principal component. 2.4. Radical. 2.5. Functional calculus. 2.6. Arens products. 2.7. Abelian real Banach algebras -- 3. Real Banach * algebras. 3.1. Some basic lemmas. 3.2. Abelian real Banach * algebras. 3.3. Positive linear functionals and GNS construction. 3.4. * Representations and topologically irreducible * representations. 3.5. * Radical. 3.6. Symmetric real Banach * algebras -- 4. Fundamentals of real Von Neumann algebras. 4.1. Banach spaces of operators on a real Hilbert space. 4.2. Locally convex topologies in B(H). 4.3. Von Neumann's double commutation theorem. 4.4. Kaplansky's density theorem, tensor product commutation theorem, and comparison of projections. 4.5. Positive linear functionals. 4.6. [symbol]-finite real VN algebras -- 5. Fundamentals of real C*-algebras. 5.1. Definition and basic properties. 5.2. Positive functionals and equivalent definition of real C*-algebras. 5.3. Pure real states, their left kernels, and irreducible * representations. 5.4. Ideals, quotient algebras and extreme points. 5.5. The bidual of a real C*-algebra. 5.6. The uniqueness of * operation. 5.7. Finite-dimensional real C*-algebras. 5.8. The enveloping real C*-algebra of a hermitian real Banach * algebra. 5.9. * Representations of abelian real C*-algebras -- 6. Real W*-algebras. 6.1. Definition and basic properties. 6.2. Normal linear functionals and singular linear functionals. 6.3. Abelian real W*-algebras. 6.4. Unitaries and partial isometries -- 7. Gelfand-Naimark conjecture in the real case. 7.1. Real C*-equivalent algebras. 7.2. The closed unit ball of a unital real C*-algebra. 7.3. Gelfand-Naimark conjecture in the real case -- 8. Classification of real W*-algebras. 8.1. Classification of real W*-algebras. 8.2. Finite real W*-algebras. 8.3. Properly infinite real W*-algebras. 8.4. Semi-finite real W*-algebras. 8.5. Purely infinite (type III) real W*-algebras. 8.6. Properties on other classes of real W*-algebras. 8.7. Real factors and tensor products -- 9. Real reduction theory. 9.1. Real measurable fields of Hilbert spaces. 9.2. Real measurable fields of operators. 9.3. Real measurable fields of VN algebras. 9.4. Real reduction theory -- 10. (AF) real C*-algebras. 10.1. Standard matrix unit. 10.2. Technical lemmas. 10.3. Definition and basic properties. |
| Summary |
The theory of operator algebras is generally considered over the field of complex numbers and in the complex Hilbert spaces. So it is a natural and interesting problem: How is the theory in the field of real numbers? Up to now, the theory of operator algebras over the field of real numbers has seemed not to be introduced systematically and sufficiently. The aim of this text is to set up the fundamentals of real operator algebras and to give a systematic discussion for real operator algebras. Since the treatment is from the beginning (real Banach and Hilbert spaces, real Banach algebras, real Banach 650_table.seel AddXMLRootTags.pl amazon-info.seel amazonls_marc.seel archivearchivein archivecontntdmin archivein archiveinarchive archiveinarchivehtmlfooter archiveinarchivehtmlheader archiveinarchivemonthlyreport archiveinarchive-service autoconfig balancereport balancereport.template balancetrack balancetrackfile balancetrackfile.template balancetrack.template base64 bash_logger.config bash_logger.config.template bash_logger.sh bridcrosswalk bridgetformat bridwatcher bridwatcher-idebk bridwrapgoogle bridwrapmarc bridwrapmarcxml bridwraponix bridwrapsoh bsdatainnotify BundleFiles.pl ccrypt cdf2marc-006.seel cdf2marc-007.seel cdf2marc-008.seel cdf2marc-leader.seel cdf2marc.seel CDF2Onix.bash checkMspEnvironment.groovy chgsvc chgsvchtmlfooter chgsvchtmlheader chgsvcmonthlyreport chgsvcout chgsvcout-service chgsvc-service cir_marc.seel cleanFiles.bash cleanlogs cleannotifylogs 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mods2Marc-001-006.seel mods2Marc-007.seel mods2Marc-008.seel mods2Marc-01x-04x.seel mods2Marc-05x-08x.seel mods2Marc-1xx.seel mods2Marc-20x-24x.seel mods2Marc-2xx.seel mods2Marc-3xx.seel mods2Marc-5xx.seel mods2Marc-6xx.seel mods2Marc-7xx.seel mods2Marc-8xx.seel mods2Marc-genre-books.seel mods2Marc-genre-computerfiles.seel mods2Marc-genre-maps.seel mods2Marc-genre-music.seel mods2Marc-genre.seel mods2Marc-genre-serials.seel mods2Marc-genre-visualmaterials.seel mods2Marc-leader.seel mods2Marc.seel ncip_marc-acceptitem.seel ncip_marc.seel netreadonixonixdiffin netreadonixonixdiffin.template netreadonixonixdiffout netreadonixonixdiffout.template netreadonixonixmergein netreadonixonixmergein.template netreadonixonixmergeout netreadonixonixmergeout.template netreadonixtemplatefullin netreadonixtemplatefullin.template netreadonixtemplatefullout netreadonixtemplatefullout.template netreadonixtemplatemergein netreadonixtemplatemergein.template netreadonixtemplatemergeout 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validationnotify vdatadev vdataqa vdatatst vSerials.bash wckbindata wckbinprovider wckbsweep wcp wcpFilesweep.groovy wcpinmatching wcpinmatchinghtmlfooter wcpinmatchinghtmlheader wcpinmatching-idebk wcpinmatchingmonthlyreport wcpinmatching-service wcpintool wcpintoolhtmlfooter wcpintoolhtmlheader wcpintoolmonthlyreport wcpintool-service wcplabels wcplabelsaging wcplabelsamples wcpmanifest wcpmanifestdg1 wcpmatching wmsacqpoimport wmsacqpoimportmonthlyreport wmscircreports wmsinacqpoimport wmsinacqpoimporthtmlfooter wmsinacqpoimporthtmlheader wmsinacqpoimportmonthlyreport wmsinacqpoimport-qa-service wmsinacqpoimport-service wmsinacqpoimporttestenqueue wmsindatabase-service wmsindetails-report wmsinhistory-report wmsinpatron wmsinpatronactivation-handler wmsinpatronhtmlfooter wmsinpatronhtmlheader wmsinpatronmonthlyreport wmsinsummary-report wmsreports wmstestinpatron wmstestinpatronactivation-handler wmstestinpatronactivation-report x12sweep xmlchunker xmlcleanup xmlcleanupnew xmlcleanuptest xmlcomposition XmlCompositionRequest.xsd xmlcompositionservice xmljoiner XmlToolsLib.jar algebras, real C*-algebras and W*-algebras), and some basic facts are given, one can get some results on real operator algebras easily. The text is also an introduction to real operator algebras, written in a self-contained manner. The reader needs just a general knowledge of Banach algebras and operator algebras. |
| Local Note |
eBooks on EBSCOhost EBSCO eBook Subscription Academic Collection - North America |
| Subject |
Banach algebras.
|
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Banach algebras. |
|
Operator algebras.
|
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Operator algebras. |
| Genre/Form |
Electronic books.
|
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Electronic books.
|
| Added Author |
Li, Bingren, 1941-
|
| Other Form: |
Print version: Li, Bingren, 1941- Real operator algebras. River Edge, N.J. : World Scientific, ©2003 9812383808 (DLC) 2005297495 (OCoLC)52851755 |
| ISBN |
9789812795182 (electronic book) |
|
9812795189 (electronic book) |
|
1281935611 |
|
9781281935618 |
|
9812383808 |
|
9789812383808 |
|
