| 11. | His specialty is functional analysis, particularly bounded operators on a Hilbert space.
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| 12. | Usually that refers to which is a Hilbert space, or to and.
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| 13. | Quotiening out degeneracy and taking the completion gives a Hilbert space
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| 14. | A Banach space finitely representable in ! 2 is a Hilbert space.
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| 15. | In a Hilbert space can be extended to subspaces of any finite dimensions.
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| 16. | Let the resulting Hilbert space be denoted by " V ".
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| 17. | The construction may also be extended to cover Banach spaces and Hilbert spaces.
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| 18. | Another area where this formulation is used is in Hilbert spaces.
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| 19. | These POVMs can be created by extending the two-dimensional Hilbert space.
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| 20. | Positive definite kernels provide a framework that encompasses some basic Hilbert space constructions.
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