# Thread: Linear and bounded operator

1. ## Linear and bounded operator

Show that
$\displaystyle {f}_{1}(x)$ = max $\displaystyle x(t)$ for $\displaystyle t\in J$, $\displaystyle J=[a,b]$

$\displaystyle {f}_{2}(x)$ = min $\displaystyle x(t)$

defines functionals on C[a,b]. Are they linear? Bounded?

2. Originally Posted by kinkong
Show that
$\displaystyle {f}_{1}(x)$ = max $\displaystyle x(t)$ for $\displaystyle t\in J$, $\displaystyle J=[a,b]$

$\displaystyle {f}_{2}(x)$ = min $\displaystyle x(t)$

defines functionals on C[a,b]. Are they linear? Bounded?
What do YOU think?

3. Originally Posted by Drexel28
What do YOU think?
Help me to get started...

4. Originally Posted by kinkong
Help me to get started...
Dude, I'm not trying to be a..whatever...but for your own benefit you should at least list your ideas and whatnot.

5. Originally Posted by Drexel28
Dude, I'm not trying to be a..whatever...but for your own benefit you should at least list your ideas and whatnot.
thanks for the concern...but the problem is i couldnt get started with it...

6. Originally Posted by kinkong
thanks for the concern...but the problem is i couldnt get started with it...
Clearly if you get the information about one you get the information about the other since you can just put a minus inside and out and change max to min. For if it's linear, is it true in general that $\displaystyle \sup (f+(-f))=\sup(f)+\sup(-f)$?

7. ## Re: Linear and bounded operator

i couldnt proceed with this question...i need some help guys..

8. ## Re: Linear and bounded operator

What's the definition of a functional?