# Linear and bounded operator

• Jun 5th 2011, 08:00 PM
kinkong
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?
• Jun 5th 2011, 08:03 PM
Drexel28
Quote:

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?
• Jun 5th 2011, 08:54 PM
kinkong
Quote:

Originally Posted by Drexel28
What do YOU think?

Help me to get started...
• Jun 5th 2011, 09:01 PM
Drexel28
Quote:

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.
• Jun 5th 2011, 09:24 PM
kinkong
Quote:

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...
• Jun 5th 2011, 09:37 PM
Drexel28
Quote:

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 $\displaystyle \sup (f+(-f))=\sup(f)+\sup(-f)$?
• Jun 18th 2011, 10:49 PM
kinkong
Re: Linear and bounded operator
i couldnt proceed with this question...i need some help guys..
• Jun 20th 2011, 12:56 AM
Ackbeet
Re: Linear and bounded operator
What's the definition of a functional?