I have 2 questions about precompactness in sequence spaces:(Doh)

1. Is A = { } is precompact in = set of all sequences converging to 0 equipped with the sup norm ?

2. Is A= { as } in ?(Shake)

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- February 26th 2011, 02:57 PMhermanniprecompactness in sequence spaces
I have 2 questions about precompactness in sequence spaces:(Doh)

1. Is A = { } is precompact in = set of all sequences converging to 0 equipped with the sup norm ?

2. Is A= { as } in ?(Shake) - February 28th 2011, 10:44 AMgirdav
1. We notice that if we have . Given an , we can find a such that . We can conclude because is precompact.

2. Let the sequence defined by .

We notice that and if . We conclude that is not precompact.