| 21. | Banach spaces are a different generalization of Hilbert spaces.
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| 22. | A further generalization for a function between Banach spaces is the Fr�chet derivative.
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| 23. | Spatial medians are defined for random vectors with values in a Banach space.
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| 24. | Since is onto and isometric, it is an isomorphism of Banach spaces.
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| 25. | The construction may also be extended to cover Banach spaces and Hilbert spaces.
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| 26. | A Banach space finitely representable in ! 2 is a Hilbert space.
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| 27. | Every Banach space is finitely representable in " c " 0.
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| 28. | The second decomposition generalizes more easily for general compact operators on Banach spaces.
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| 29. | Let X be a Banach space and let 1 \ leq \ lambda.
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| 30. | Some generalizations to Banach spaces and more general topological vector spaces are possible.
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