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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| Main Author: | |
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| Format: | Article |
| Language: | deu |
| Published: |
Ivan Franko National University of Lviv
2013-04-01
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| Series: | Математичні Студії |
| Subjects: | |
| Online Access: | http://matstud.org.ua/texts/2013/39_1/21-28.pdf |
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| Summary: | 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. |
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| ISSN: | 1027-4634 |