Topological classification of pairs of counter linear maps (in Ukrainian)
We consider pairs of linear mappings $(cal A,cal B)$ of theformsmallskipcenterline{$pud{V}{W} {cal A}{cal B} $} oi in which $V$ and $W$ arefinite dimensional unitary or Euclidean spaces over$mathbb{C}$ or $mathbb{R}$, respectively. Let $(cal A,calB)$ be transformed tosmallskipcenterline{$ pud{V'...
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| Format: | Article |
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Ivan Franko National University of Lviv
2013-04-01
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| Series: | Математичні Студії |
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| Online Access: | http://matstud.org.ua/texts/2013/39_1/21-28.pdf |
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| author | T. V. Rybalkina |
| author_facet | T. V. Rybalkina |
| author_sort | T. V. Rybalkina |
| collection | DOAJ |
| description | We consider pairs of linear mappings $(cal A,cal B)$ of theformsmallskipcenterline{$pud{V}{W} {cal A}{cal B} $} oi in which $V$ and $W$ arefinite dimensional unitary or Euclidean spaces over$mathbb{C}$ or $mathbb{R}$, respectively. Let $(cal A,calB)$ be transformed tosmallskipcenterline{$ pud{V'}{W'} {cal A'}{cal B'} $} oi by bijections$varphi_1colon Vo V'$ and $varphi_2colon Wo W'$. We saythat $(cal A,cal B)$ and $(cal A',cal B')$ are linearlyequivalent if $varphi_1$ and $varphi_2$ are linear bijectionsand topologically equivalent if $ varphi_1 $ and $ varphi_2 $are homeomorphisms. We prove that $(cal A,cal B)$ and $(calA',cal B')$ are topologically equivalent if and only if theirregular parts are topologically equivalent and their singularparts are linearly equivalent. |
| format | Article |
| id | doaj-art-af44b60944ba451fbfdca743de650d0f |
| institution | Kabale University |
| issn | 1027-4634 |
| language | deu |
| publishDate | 2013-04-01 |
| publisher | Ivan Franko National University of Lviv |
| record_format | Article |
| series | Математичні Студії |
| spelling | doaj-art-af44b60944ba451fbfdca743de650d0f2025-08-20T03:38:38ZdeuIvan Franko National University of LvivМатематичні Студії1027-46342013-04-013912128Topological classification of pairs of counter linear maps (in Ukrainian)T. V. RybalkinaWe consider pairs of linear mappings $(cal A,cal B)$ of theformsmallskipcenterline{$pud{V}{W} {cal A}{cal B} $} oi in which $V$ and $W$ arefinite dimensional unitary or Euclidean spaces over$mathbb{C}$ or $mathbb{R}$, respectively. Let $(cal A,calB)$ be transformed tosmallskipcenterline{$ pud{V'}{W'} {cal A'}{cal B'} $} oi by bijections$varphi_1colon Vo V'$ and $varphi_2colon Wo W'$. We saythat $(cal A,cal B)$ and $(cal A',cal B')$ are linearlyequivalent if $varphi_1$ and $varphi_2$ are linear bijectionsand topologically equivalent if $ varphi_1 $ and $ varphi_2 $are homeomorphisms. We prove that $(cal A,cal B)$ and $(calA',cal B')$ are topologically equivalent if and only if theirregular parts are topologically equivalent and their singularparts are linearly equivalent.http://matstud.org.ua/texts/2013/39_1/21-28.pdfpairs of counter mapstopological equivalence |
| spellingShingle | T. V. Rybalkina Topological classification of pairs of counter linear maps (in Ukrainian) Математичні Студії pairs of counter maps topological equivalence |
| title | Topological classification of pairs of counter linear maps (in Ukrainian) |
| title_full | Topological classification of pairs of counter linear maps (in Ukrainian) |
| title_fullStr | Topological classification of pairs of counter linear maps (in Ukrainian) |
| title_full_unstemmed | Topological classification of pairs of counter linear maps (in Ukrainian) |
| title_short | Topological classification of pairs of counter linear maps (in Ukrainian) |
| title_sort | topological classification of pairs of counter linear maps in ukrainian |
| topic | pairs of counter maps topological equivalence |
| url | http://matstud.org.ua/texts/2013/39_1/21-28.pdf |
| work_keys_str_mv | AT tvrybalkina topologicalclassificationofpairsofcounterlinearmapsinukrainian |