| 21. | The local isometry constraint prevents the objective function from going to infinity.
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| 22. | The concept of partial isometry can be defined in other equivalent ways.
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| 23. | This is clarifying when categorizing isometry groups, see below.
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| 24. | This map is an isometry, so it is continuous.
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| 25. | Wold decomposition characterizes proper isometries acting on a Hilbert space.
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| 26. | The proof is easy if one assumes the classification of plane isometries.
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| 27. | Usually one takes G to be the full isometry group of X.
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| 28. | An isometry exists between the Hilbert spaces associated with these two kernels:
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| 29. | Every metric space has a unique ( up to isometry ) dense subset.
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| 30. | A partially defined isometric operator with closed domain is called a partial isometry.
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