Classical Banach spaces |
| 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. |
![{\displaystyle \operatorname {BV} ([a,b])}](//wikimedia.org/api/rest_v1/media/math/render/svg/8f6474e123b8d06d5989e779c17b9084f2ba8314) |
? | No | Yes |
 |
![{\displaystyle =V_{f}([a,b])+\lim \nolimits _{x\to a^{+}}f(x)}](//wikimedia.org/api/rest_v1/media/math/render/svg/25115dbc151a6a6ca22cd714e3c0a588ae8c97ab) |
is the total variation of  |
![{\displaystyle \operatorname {NBV} ([a,b])}](//wikimedia.org/api/rest_v1/media/math/render/svg/97eacd1b77125924adb034d279f23ccb1aae4cfc) |
? | No | Yes |
 |
![{\displaystyle =V_{f}([a,b])}](//wikimedia.org/api/rest_v1/media/math/render/svg/3978b950e1c45a40b89de47e166dff3e3f640f90) |
consists of functions such that  |
![{\displaystyle \operatorname {AC} ([a,b])}](//wikimedia.org/api/rest_v1/media/math/render/svg/c1215f6bb4f5dcce36b275a1038200a2da63ffc8) |
![{\displaystyle \mathbb {F} +L^{\infty }([a,b])}](//wikimedia.org/api/rest_v1/media/math/render/svg/3ef63fd9a8ef0c7df601ba2aa141815ea86073da) | No | Yes |
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![{\displaystyle =V_{f}([a,b])+\lim \nolimits _{x\to a^{+}}f(x)}](//wikimedia.org/api/rest_v1/media/math/render/svg/25115dbc151a6a6ca22cd714e3c0a588ae8c97ab) |
Isomorphic to the Sobolev space ![{\displaystyle W^{1,1}([a,b]).}](//wikimedia.org/api/rest_v1/media/math/render/svg/a982993a7010fe121285b640c096068e79e74874) |
![{\displaystyle C^{n}([a,b])}](//wikimedia.org/api/rest_v1/media/math/render/svg/7e5f2c81e52a668fa74a30946eac00229b1d642f) |
![{\displaystyle \operatorname {rca} ([a,b])}](//wikimedia.org/api/rest_v1/media/math/render/svg/b8788ca02e303b567e9d47a44b0fd48a574ddbfb) | No | No |
 |
![{\displaystyle =\sum _{i=0}^{n}\sup \nolimits _{x\in [a,b]}\left|f^{(i)}(x)\right|}](//wikimedia.org/api/rest_v1/media/math/render/svg/3cc9f7a9abc638e6fe431d6f36760dbd074b3019) |
Isomorphic to essentially by Taylor's theorem. |