#### Heidi

Summary
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.

Related Topology and Analysis News on Phys.org

#### WWGD

Gold Member
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.

#### Heidi

is there a problem for everybody? (it works for me).

#### fresh_42

Mentor
2018 Award
Didn't work here either for the first time. The second time worked. Don't ask me why. FF-effect maybe.

#### WWGD

Gold Member
What is $\chi$?

#### Heidi

it may be identified with R`^d

#### Heidi

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> ?

### Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving