Article PDF
Avoid common mistakes on your manuscript.
References
Dunford, N., Schwartz, J. T.: Linear operators. II. Spectral theory. New York, London: Interscience 1963
Halmos, P.R.: Introduction to Hilbert space and the theory of spectral multiplicity. New York: Chelsea 1951
Hilbert, D.: Grundzüge einer allgemeinen Theorie der linearen Integralgleichungen. I–VI. IV. Nachr. Akad. Wiss. Göttingen. Math. Phys. K.l.
Hilbert, D.: Grundzüge einer allgemeinen Theorie der linearen Integralgleichungen. I–VI. Nachr. Akad. Wiss. Göttingen. Math. Phys. Kl. IV, 157–227 (1906)
Kato, T.: Perturbation theory for linear operators. Grundlehren der mathematischen Wissenschaften, Band 132. Berlin, Heidelberg, New York: Springer 1976
Lengyel, B.A., Stone, M.H.: Elementary proof of the spectral theorem. Ann. of Math.37, 853–864 (1936)
Masson, D., McClary, W.K.: Classes ofC ∞-vectors and essential self-adjointness. J. Functional Analysis10, 19–32 (1972)
Nelson, E.: Analytic vectors. Ann. of Math.70, 572–615 (1959)
Neumann, J. v.: Allgemeine Eigenwerttheorie-hermitescher Funktionaloperatoren. Math. Ann.102, 49–131 (1929)
Radjavi, H., Rosenthal, P.: Invariant subspaces. Ergebnisse der Mathematik und ihre Grenzgebiete, Band 77. Berlin, Heidelberg, New York: Springer 1973
Weidmann, J.: Lineare Operatoren in Hilberträumen. Mathematische Leitfäden. Stuttgart: Teubner 1976
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Leinfelder, H. A geometric proof of the spectral theorem for unbounded self-adjoint operators. Math. Ann. 242, 85–96 (1979). https://doi.org/10.1007/BF01420484
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01420484