Perturbation of continuous spectra by unbounded operators, I

Shige Toshi KURODA

doi:10.2969/jmsj/01130247

Shige Toshi KURODA

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ジャーナルフリー

1959 年 11 巻 3 号 p. 247-262

DOI https://doi.org/10.2969/jmsj/01130247

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Published: 1959 Received: 1959/03/14 Available on J-STAGE: 2006/08/29 Accepted: - Advance online publication: - Revised: -
訂正情報
訂正日: 2006/08/29 訂正理由: - 訂正箇所: 引用文献情報訂正内容: Wrong : 1) N. I. Achieser and I. M. Glasmann, Theorie der linearen Operatoren im Hilbert-Raum, Berlin, 1954.
2) E. Heinz, Beiträge zur Störungstheorie der Spektralzerlegung, Math. Ann. 123 (1951), 415-438.
3) E. Hille, Functional analysis and semi-groups, New York, (1948).
4) T. Kato, On finite-dimensional perturbations of self-adjoint operators, J. Math. Soc. Japan, 9 (1957), 239-249.
5) T. Kato, Perturbation of continuous spectra by trace class operators, Proc. Japan Acad., 33 (1957), 260-264.
6) T. Kato, Scattering operators and perturbation of continuous spectra, Sûgaku 9 (1957), 75-84 (in Japanese).
7) T. Kato, Fundamental properties of Hamiltonian operators of Schrodinger type, Trans. Amer. Math. Soc., 70 (1951), 195-211.
8) T. Kato, Notes on some inequalities for linear operators, Math. Ann., 125 (1952), 208-212.
9) S. T. Kuroda, On a theorem of Weyl-von Neumann, Proc. Japan Acad., 34 (1958), 11-15.
10) S. T. Kuroda, On the existence and the unitary property of the scattering operator, to be published in Nuovo Cimento, 12 (1959).
11) F. Rellich, Störungstheorie der Spektralzerlegung, III. Mitteilung, Math. Ann. 116 (1939), 555-570.
12) M. Rosenblum, Perturbation of the continuous spectrum and unitary equivalence, Pacif. J. Math., 7 (1957), 997-1010.
13) R. Schatten, A theory of cross spaces, Ann. Math. Studies, Princeton, 1950.
14) M. H. Stone, Linear transformations in Hilbert space, Now York, 1932.
15) J. von Neumann, Über adjungierte Funktionaloperatoren, Ann. of Math., 33 (1932), 294-310.

Right : [1] N. I. Achieser and I. M. Glasmann, Theorie der linearen Operatoren im Hilbert-Raum, Berlin, 1954.
[2] E. Heinz, Beiträge zur Störungstheorie der Spektralzerlegung, Math. Ann. 123 (1951), 415-438.
[3] E. Hille, Functional analysis and semi-groups, New York, (1948).
[4] T. Kato, On finite-dimensional perturbations of self-adjoint operators, J. Math. Soc. Japan, 9 (1957), 239-249.
[5] T. Kato, Perturbation of continuous spectra by trace class operators, Proc. Japan Acad., 33 (1957), 260-264.
[6] T. Kato, Scattering operators and perturbation of continuous spectra, Sûgaku 9 (1957), 75-84 (in Japanese).
[7] T. Kato, Fundamental properties of Hamiltonian operators of Schrödinger type, Trans. Amer. Math. Soc., 70 (1951), 195-211.
[8] T. Kato, Notes on some inequalities for linear operators, Math. Ann., 125 (1952), 208-212.
[9] S. T. Kuroda, On a theorem of Weyl-von Neumann, Proc. Japan Acad., 34 (1958), 11-15.
[10] S. T. Kuroda, On the existence and the unitary property of the scattering operator, to be published in Nuovo Cimento, 12 (1959).
[11] F. Rellich, Störungstheorie der Spektralzerlegung, III. Mitteilung, Math. Ann. 116 (1939), 555-570.
[12] M. Rosenblum, Perturbation of the continuous spectrum and unitary equivalence, Pacif. J. Math., 7 (1957), 997-1010.
[13] R. Schatten, A theory of cross spaces, Ann. Math. Studies, Princeton, 1950.
[14] M. H. Stone, Linear transformations in Hilbert space, Now York, 1932.
[15] J. von Neumann, Über adjungierte Funktionaloperatoren, Ann. of Math., 33 (1932), 294-310.

訂正日: 2006/08/29 訂正理由: - 訂正箇所: PDFファイル訂正内容: -

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