B Quadratic form identity?

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could you explain why this equality is a quadratic form identity?
Summary: could you explain why this equality is a quadratic form identity?

i read this equality (4.26) here w depends on two variables. it is written that if B is bounded (L2) then it is a quadratic form identity on S. what does it mean? is it related to the two variables?
next the author writes that if w is continuous in the variable we have an identity operator on L2(X). does il mean that for every vector the two terms give a same result? how to prove that?

thanks a lot.
 

WWGD

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Summary: could you explain why this equality is a quadratic form identity?

i read this equality (4.26) here w depends on two variables. it is written that if B is bounded (L2) then it is a quadratic form identity on S. what does it mean? is it related to the two variables?
next the author writes that if w is continuous in the variable we have an identity operator on L2(X). does il mean that for every vector the two terms give a same result? how to prove that?

thanks a lot.
Link does not seem to be working. Please use a screenshot or something else.
 
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is there a problem for everybody? (it works for me).
 

fresh_42

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Didn't work here either for the first time. The second time worked. Don't ask me why. FF-effect maybe.


1567807416884.png

1567807189576.png


1567807336013.png
 

WWGD

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What is ##\chi##?
 
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it may be identified with R`^d
 
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Does it mean in the first case that we have a same way to associate a complex number to each couple f1, f2 of function? the dirac notation would be <f1|B|f2>
and in the second case the same function noted B|f> ?
 

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