Linear and bounded operator

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June 5th 2011, 08:00 PM
kinkong

Linear and bounded operator

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

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

defines functionals on C[a,b]. Are they linear? Bounded?
June 5th 2011, 08:03 PM
Drexel28

Quote:

Originally Posted by kinkong

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

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

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

What do YOU think?
June 5th 2011, 08:54 PM
kinkong

Quote:

Originally Posted by Drexel28

What do YOU think?

Help me to get started...
June 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.
June 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...
June 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 $\sup (f+(-f))=\sup(f)+\sup(-f)$ ?
June 18th 2011, 10:49 PM
kinkong

Re: Linear and bounded operator

i couldnt proceed with this question...i need some help guys..
June 20th 2011, 12:56 AM
Ackbeet

Re: Linear and bounded operator

What's the definition of a functional?

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