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A question on linear integral equation about non degenerated bilinear form

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0

$begingroup$

Let $X$ be a Banach Space , $Xsubseteq H,barX=H$,where $H$ is a Hilbert space $i:=Xto H$ defined by $i(x)=x$ and is continuous. Define $langle x,yrangle=langle ix,iyrangle$ then $langle X,X,(.,.) rangle$ to be a dual system.

Dual system definition :

from linear integral equations by rainer kress

Here I am trying to prove first Bilinear form. It's okay How to prove non-degenerate thing and dual system thing. Can someone explain this to me?

Thank you.

functional-analysis vector-spaces compact-operators bilinear-form

share|cite|improve this question

edited Mar 16 at 11:55

Inverse Problem

asked Mar 15 at 12:14

Inverse ProblemInverse Problem

1,028918

$endgroup$

add a comment | 

0

$begingroup$

Let $X$ be a Banach Space , $Xsubseteq H,barX=H$,where $H$ is a Hilbert space $i:=Xto H$ defined by $i(x)=x$ and is continuous. Define $langle x,yrangle=langle ix,iyrangle$ then $langle X,X,(.,.) rangle$ to be a dual system.

Dual system definition :

from linear integral equations by rainer kress

Here I am trying to prove first Bilinear form. It's okay How to prove non-degenerate thing and dual system thing. Can someone explain this to me?

Thank you.

functional-analysis vector-spaces compact-operators bilinear-form

share|cite|improve this question

edited Mar 16 at 11:55

Inverse Problem

asked Mar 15 at 12:14

Inverse ProblemInverse Problem

1,028918

$endgroup$

add a comment | 

$begingroup$

Let $X$ be a Banach Space , $Xsubseteq H,barX=H$,where $H$ is a Hilbert space $i:=Xto H$ defined by $i(x)=x$ and is continuous. Define $langle x,yrangle=langle ix,iyrangle$ then $langle X,X,(.,.) rangle$ to be a dual system.

Dual system definition :

from linear integral equations by rainer kress

Here I am trying to prove first Bilinear form. It's okay How to prove non-degenerate thing and dual system thing. Can someone explain this to me?

Thank you.

functional-analysis vector-spaces compact-operators bilinear-form

share|cite|improve this question

edited Mar 16 at 11:55

Inverse Problem

asked Mar 15 at 12:14

Inverse ProblemInverse Problem

1,028918

$endgroup$

share|cite|improve this question

edited Mar 16 at 11:55

Inverse Problem

asked Mar 15 at 12:14

Inverse ProblemInverse Problem

1,028918

share|cite|improve this question

edited Mar 16 at 11:55

Inverse Problem

asked Mar 15 at 12:14

Inverse ProblemInverse Problem

1,028918

asked Mar 15 at 12:14

Inverse ProblemInverse Problem

1,028918

asked Mar 15 at 12:14

Inverse ProblemInverse Problem

1,028918