| 11. | If is a Hilbert space, then by the Riesz representation theorem, all matrix coefficients have the form
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| 12. | For example, the Riesz representation theorem was independently established by Maurice Fr�chet and Frigyes Riesz in 1907.
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| 13. | Additionally, " [ I ] n the general case, von Neumann proved the following basic representation theorem.
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| 14. | Another corollary is the Riesz representation theorem for states on the continuous functions on a metrizable compact Hausdorff space.
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| 15. | This construction and representation theorem is a special case of the more general result for modal algebras and modal frames.
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| 16. | If B is a Hilbert space, then, by the Riesz representation theorem, any such f has the form
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| 17. | The Riesz representation theorem states that every continuous linear functional on is of the form for a uniquely defined vector in.
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| 18. | Well known results like the representation theorem for Boolean algebras and Stone duality fall under the umbrella of classical algebraic logic.
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| 19. | This line of research leads to various " representation theorems ", often collected under the label of Stone duality.
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| 20. | The idea is to first establish the continuous functional calculus then pass to measurable functions via the Riesz-Markov representation theorem.
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