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linear_operator_space [2013/09/17 13:46] nikolaj |
linear_operator_space [2014/03/21 11:11] 127.0.0.1 external edit |
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| ===== Linear operator space ===== | ===== Linear operator space ===== | ||
| - | ==== Definition ==== | + | ==== Set ==== |
| - | | @#88DDEE: $X,Y$...left $\mathcal R$-module | | + | | @#55CCEE: context | @#55CCEE: $X,Y$...left $\mathcal R$-module | |
| - | | @#FFBB00: $\langle\mathrm{Hom}(X,Y),+,\cdot \rangle \in \mathcal L(X,Y)$ | | + | | @#FFBB00: definiendum | @#FFBB00: $\langle\mathrm{Hom}(X,Y),+,\cdot \rangle \in \mathcal L(X,Y)$ | |
| - | | @#88DDEE: $+:\mathrm{Hom}(X,Y)\times \mathrm{Hom}(X,Y)\to \mathrm{Hom}(M,N)$ | | + | | @#55CCEE: context | @#55CCEE: $+:\mathrm{Hom}(X,Y)\times \mathrm{Hom}(X,Y)\to \mathrm{Hom}(M,N)$ | |
| - | | @#88DDEE: $\cdot : \mathcal R\times\mathrm{Hom}(X,Y)\to\mathrm{Hom}(X,Y)$ | | + | | @#55CCEE: context | @#55CCEE: $\cdot : \mathcal R\times\mathrm{Hom}(X,Y)\to\mathrm{Hom}(X,Y)$ | |
| | $ v\in M $ | | | $ v\in M $ | | ||
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| | $A,B \in \mathrm{Hom}(X,Y)$ | | | $A,B \in \mathrm{Hom}(X,Y)$ | | ||
| - | | @#55EE55: $(r \cdot A+s \cdot B)\ v = r\ (A\ v) + s\ (B\ v) $ | | + | | @#55EE55: postulate | @#55EE55: $(r \cdot A+s \cdot B)\ v = r\ (A\ v) + s\ (B\ v) $ | |
| ==== Discussion ==== | ==== Discussion ==== | ||
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| Wikipedia: [[https://en.wikipedia.org/wiki/Left_module#Submodules_and_homomorphisms|Module]] | Wikipedia: [[https://en.wikipedia.org/wiki/Left_module#Submodules_and_homomorphisms|Module]] | ||
| ==== Parents ==== | ==== Parents ==== | ||
| - | === Requirements === | + | === Context === |
| [[Left module homomorphism]] | [[Left module homomorphism]] | ||
