Hi,
how to prove, that for and the embedding is not compact?
I've got a hint, to use the sequence with . So, I should prove, that the space is not sequentially compact.
Please can you help me?
Bye,
Alexander
Hi,
thank you for your hints. By definition, a sequence in a banach space is weakly convergent to an element , if for every , where denotes the dual space of .
The dual space of is the space of all linear functions . So I have to prove that there exists a , with for all ?
( )
How to find this ?
Now to the other statement:
Do I have to prove that there is no with ?
Bye,
Alexander