Automatic Boundedness of Adjointable Operators on Barreled Vh-Spaces
| dc.contributor.author | Ay, Serdar | |
| dc.date.accessioned | 2024-07-05T15:16:28Z | |
| dc.date.available | 2024-07-05T15:16:28Z | |
| dc.date.issued | 2022 | |
| dc.description.abstract | We consider the space of adjointable operators on barreled VH (Vector Hilbert) spaces and show that such operators are automatically bounded. This generalizes the well known corresponding result for locally Hilbert C*-modules. We pick a consequence of this result in the dilation theory of VH-spaces and show that, when barreled VH-spaces are considered, a certain boundedness condition for the existence of VH-space linearisations, equivalently, of reproducing kernel VH-spaces, is automatically satisfied. | en_US |
| dc.identifier.doi | 10.1007/s11785-021-01184-6 | |
| dc.identifier.issn | 1661-8254 | |
| dc.identifier.issn | 1661-8262 | |
| dc.identifier.scopus | 2-s2.0-85122996405 | |
| dc.identifier.uri | https://doi.org/10.1007/s11785-021-01184-6 | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14411/1642 | |
| dc.language.iso | en | en_US |
| dc.publisher | Springer Basel Ag | en_US |
| dc.relation.ispartof | Complex Analysis and Operator Theory | |
| dc.rights | info:eu-repo/semantics/openAccess | en_US |
| dc.subject | Ordered *-space | en_US |
| dc.subject | Admissible space | en_US |
| dc.subject | VH-space | en_US |
| dc.subject | Barreled VH-space | en_US |
| dc.subject | Adjointable operators | en_US |
| dc.subject | Bounded operators | en_US |
| dc.subject | Positive semidefinite kernel | en_US |
| dc.subject | Invariant kernel | en_US |
| dc.subject | Linearisation | en_US |
| dc.subject | Reproducing kernel | en_US |
| dc.subject | *-Representation | en_US |
| dc.subject | Locally C*-algebra | en_US |
| dc.subject | Hilbert locally C*-module | en_US |
| dc.title | Automatic Boundedness of Adjointable Operators on Barreled Vh-Spaces | en_US |
| dc.type | Article | en_US |
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| gdc.coar.type | text::journal::journal article | |
| gdc.description.department | Atılım University | en_US |
| gdc.description.departmenttemp | [Ay, Serdar] Atilim Univ, Dept Math, TR-06830 Ankara, Turkey | en_US |
| gdc.description.issue | 1 | en_US |
| gdc.description.publicationcategory | Makale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı | en_US |
| gdc.description.scopusquality | Q3 | |
| gdc.description.volume | 16 | en_US |
| gdc.description.wosquality | Q2 | |
| gdc.identifier.openalex | W3192691521 | |
| gdc.identifier.wos | WOS:000743016200002 | |
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| gdc.oaire.keywords | Mathematics - Functional Analysis | |
| gdc.oaire.keywords | FOS: Mathematics | |
| gdc.oaire.keywords | Primary 46A08, 47L05, 47L10, Secondary 06F30, 43A35, 46L89, 47A20 | |
| gdc.oaire.keywords | Functional Analysis (math.FA) | |
| gdc.oaire.keywords | Hilbert locally \(C^*\)-module | |
| gdc.oaire.keywords | positive semidefinite kernel | |
| gdc.oaire.keywords | Other ``noncommutative'' mathematics based on \(C^*\)-algebra theory | |
| gdc.oaire.keywords | locally \(C^*\)-algebra | |
| gdc.oaire.keywords | barreled VH space | |
| gdc.oaire.keywords | Barrelled spaces, bornological spaces | |
| gdc.oaire.keywords | ordered \(*\)-space | |
| gdc.oaire.keywords | Ordered topological structures | |
| gdc.oaire.keywords | adjointable operator | |
| gdc.oaire.keywords | Dilations, extensions, compressions of linear operators | |
| gdc.oaire.keywords | Linear spaces of operators | |
| gdc.oaire.keywords | Positive definite functions on groups, semigroups, etc. | |
| gdc.oaire.keywords | VH space | |
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| gdc.virtual.author | Ay, Serdar | |
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