Classical Banach spaces
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Dual space |
Reflexive |
weakly sequentially complete |
Norm |
Notes
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Yes |
Yes
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Euclidean space
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Yes |
Yes
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Yes |
Yes
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Yes |
Yes
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No |
Yes
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No |
No
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No |
No
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No |
No
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Isomorphic but not isometric to
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No |
Yes
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Isometrically isomorphic to
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No |
Yes
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Isometrically isomorphic to
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No |
No
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Isometrically isomorphic to
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No |
No
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Isometrically isomorphic to
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No |
No
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No |
No
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? |
No |
Yes
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? |
No |
Yes
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A closed subspace of
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? |
No |
Yes
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A closed subspace of
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Yes |
Yes
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No |
Yes
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The dual is if is -finite.
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? |
No |
Yes
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is the total variation of
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? |
No |
Yes
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consists of functions such that
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No |
Yes
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Isomorphic to the Sobolev space
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No |
No
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Isomorphic to essentially by Taylor's theorem.
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