| 1. | Let be a Banach space and be a normed vector space.
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| 2. | Let and be Banach spaces and be a continuous linear operator.
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| 3. | The definition of weak convergence can be extended to Banach spaces.
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| 4. | It is necessary that the spaces in question be Banach spaces.
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| 5. | Banach space obtained by the real interpolation method with parameters and.
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| 6. | More generally, this holds in any uniformly convex Banach space.
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| 7. | Every finite-dimensional normed space over or is a Banach space.
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| 8. | The Banach Steinhaus theorem is not limited to Banach spaces.
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| 9. | The chain rule is also valid for Fr�chet derivatives in Banach spaces.
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| 10. | Two prominent examples occur for Banach spaces and Hilbert spaces.
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