determine whether w={f:f(x)greater than or equal to 0} is a subspace of C, the set is continuous functions on the real numbers

Printable View

- February 21st 2011, 05:41 PMrabih2011subspaces
determine whether w={f:f(x)greater than or equal to 0} is a subspace of C, the set is continuous functions on the real numbers

- February 21st 2011, 05:58 PMDrSteve
If f is in w, think about the function -f.

- February 21st 2011, 08:57 PMRaoh
In other words,is closed under scalar multiplication ?

- February 21st 2011, 11:05 PMFernandoRevilla

No, it isn't. Look at**DrSteve**'s post. For example choose for all then, however . That is, .

Fernando Revilla - February 22nd 2011, 03:35 AMAckbeet
- February 22nd 2011, 11:43 AMRaoh
My question was meant to help the OP'er.

- February 22nd 2011, 12:30 PMFernandoRevilla

Sorry, by error I thought your post was from the original poster. :)

Fernando Revilla - February 22nd 2011, 02:38 PMDrSteve
Wow - it's not too hard to get thanked around here - very polite group!