The fundamental and weakly continuous properties in complemented topological algebras
We give conditions so that a certain left complemented algebra turns to be a fundamental one. In the case when the only minimal closed right ideals of a certain complemented algebra (E, ⊥) are axial, namely they have the form eE with e a special element and its vector complementor is continuous, the...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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University Constantin Brancusi of Targu-Jiu
2019-09-01
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| Series: | Surveys in Mathematics and its Applications |
| Subjects: | |
| Online Access: | http://www.utgjiu.ro/math/sma/v14/p14_12.pdf |
| _version_ | 1811247226872135680 |
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| author | Marina Haralampidou Konstantinos Tzironis |
| author_facet | Marina Haralampidou Konstantinos Tzironis |
| author_sort | Marina Haralampidou |
| collection | DOAJ |
| description | We give conditions so that a certain left complemented algebra turns to be a fundamental one. In the case when the only minimal closed right ideals of a certain complemented algebra (E, ⊥) are axial, namely they have the form eE with e a special element and its vector complementor is continuous, then ⊥ is weakly continuous. Moreover, conditions are supplied so that a left precomplemented locally m-convex algebra turns to be a complemented one. |
| first_indexed | 2024-04-12T15:05:14Z |
| format | Article |
| id | doaj.art-309e3222e6cc4ad89a99740b1776cf3a |
| institution | Directory Open Access Journal |
| issn | 1843-7265 1842-6298 |
| language | English |
| last_indexed | 2024-04-12T15:05:14Z |
| publishDate | 2019-09-01 |
| publisher | University Constantin Brancusi of Targu-Jiu |
| record_format | Article |
| series | Surveys in Mathematics and its Applications |
| spelling | doaj.art-309e3222e6cc4ad89a99740b1776cf3a2022-12-22T03:27:57ZengUniversity Constantin Brancusi of Targu-JiuSurveys in Mathematics and its Applications1843-72651842-62982019-09-0114 (2019)219229The fundamental and weakly continuous properties in complemented topological algebrasMarina Haralampidou0Konstantinos Tzironis1Department of Mathematics, National and Kapodistrian University of Athens, Panepistimioupolis, Athens 15784, GreeceDepartment of Mathematics, National and Kapodistrian University of Athens, Panepistimioupolis, Athens 15784, GreeceWe give conditions so that a certain left complemented algebra turns to be a fundamental one. In the case when the only minimal closed right ideals of a certain complemented algebra (E, ⊥) are axial, namely they have the form eE with e a special element and its vector complementor is continuous, then ⊥ is weakly continuous. Moreover, conditions are supplied so that a left precomplemented locally m-convex algebra turns to be a complemented one.http://www.utgjiu.ro/math/sma/v14/p14_12.pdfcomplemented vector spaceleft complemented algebratopologically simple algebrafundamental topological linear spacefundamental topological algebraaxially closed element(weakly) continuous complementor |
| spellingShingle | Marina Haralampidou Konstantinos Tzironis The fundamental and weakly continuous properties in complemented topological algebras Surveys in Mathematics and its Applications complemented vector space left complemented algebra topologically simple algebra fundamental topological linear space fundamental topological algebra axially closed element (weakly) continuous complementor |
| title | The fundamental and weakly continuous properties in complemented topological algebras |
| title_full | The fundamental and weakly continuous properties in complemented topological algebras |
| title_fullStr | The fundamental and weakly continuous properties in complemented topological algebras |
| title_full_unstemmed | The fundamental and weakly continuous properties in complemented topological algebras |
| title_short | The fundamental and weakly continuous properties in complemented topological algebras |
| title_sort | fundamental and weakly continuous properties in complemented topological algebras |
| topic | complemented vector space left complemented algebra topologically simple algebra fundamental topological linear space fundamental topological algebra axially closed element (weakly) continuous complementor |
| url | http://www.utgjiu.ro/math/sma/v14/p14_12.pdf |
| work_keys_str_mv | AT marinaharalampidou thefundamentalandweaklycontinuouspropertiesincomplementedtopologicalalgebras AT konstantinostzironis thefundamentalandweaklycontinuouspropertiesincomplementedtopologicalalgebras AT marinaharalampidou fundamentalandweaklycontinuouspropertiesincomplementedtopologicalalgebras AT konstantinostzironis fundamentalandweaklycontinuouspropertiesincomplementedtopologicalalgebras |