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Homework Help: Form of a linear map

  1. Feb 21, 2008 #1

    quasar987

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    [SOLVED] form of a linear map

    1. The problem statement, all variables and given/known data
    Say E is a linear space (not necessarily of finite dimension), and R is the real numbers. Say we have a (contiuous) linear form T from E x R to R. Can we say T is of such and such a form? Particularily, can we say that T=g1+g2 where g1:E-->R and g2:R-->R are linear forms?
     
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  3. Feb 21, 2008 #2

    Dick

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    Sure. Take (x,y) in ExR. Define g1(x,y)=T(x,0) and g2(x,y)=T(0,y). Is that what you meant? Doesn't that work?
     
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