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Symmetric linear operators on a Banach space

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References

  1. For accounts of this theory from various points of view reference may be made to (1) Modern Analysis, byE. T. Whittaker andG. N. Watson, (4th edition, Cambridge, 1927), 223–229; (2) Methoden der Mathematischen Physik, I, byR. Courant andD. Hilbert (Springer, Berlin, 1931), 104–118; (3) Theory of Lie Groups, I, byC. Chevalley (Princeton, 1946), 205–209.

  2. The proof of the result without this additional assumption is due toF. Riesz. Acta Math., 41 (1918), 71–98. Reference may also be made toS. Banach, Operations Lineaires (Warsaw, 1932), Ch. 10.

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  3. The observation that complex-variable theory may be used in this manner is due toF. Riesz, “Systèmes d'équations linéaires à une infinité d'inconnues” (Paris, 1913), p. 116–120.

  4. Wiener Sitzungsberichte, IIa,128 (1919), 1083–1121.

  5. It is however totally continuous on the adjoint space, soe for instance Banach, loc. cit., Operations Lineaires (Warsaw, 1932), Ch. 10 p. 100.

  6. SeeBanach, loc. cit., Operations Lineaires (Warsaw, 1932), Ch. 10 p. 151, andF. Hausdorff, J. f. d. reine und angewandte Math., 167 (1932), pp. 294–311. Reference may also be made to a paper to appear in Mat. Sbornik (Recueil Math.), where I have considered normal solubility from a general point of view.

  7. See for instancevan der Waerden, “Moderne Algebra”, Bd. II (Springer, 1940), §§ 116–118.

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  1. Ibadan, Nigeria

    F. V. Atkinson

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  1. F. V. Atkinson
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Atkinson, F.V. Symmetric linear operators on a Banach space. Monatshefte für Mathematik 53, 278–297 (1949). https://doi.org/10.1007/BF01302597

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