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On the perturbation of linear operators in Banach and Hilbert spaces
Noboru OKAZAWA
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Noboru OKAZAWA
Department of Mathematics Faculty of Science Science University of Tokyo
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1982 Volume 34 Issue 4 Pages 677-701
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- Published: 1982 Received: April 07, 1980 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Correction information
Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) H. Behncke and H. Focke, Stability of deficiency indices, Proc. Roy. Soc. Edinburgh, Sect. A, 78 (1977), 119-127.
2) P. R. Chernoff, Perturbations of dissipative operators with relative bound one, Proc. Amer. Math. Soc., 33 (1972), 72-74.
3) W. N. Everitt and M. Giertz, Inequalities and separation for Schrödinger type operators in L2(Rn), Proc. Roy. Soc. Edinburgh, Sect. A, 79 (1977), 257-265.
4) W. G. Faris and R. B. Lavine, Commutators and selfadjointness of Hamiltonian operators, Comm. Math. Phys., 35 (1974), 39-48.
5) S. Goldberg, Unbounded linear operators, Theory and applications, Series in Higher Math., McGraw-Hill, New York, 1966.
6) K. Gustafson, A perturbation lemma, Bull. Amer. Math. Soc., 72 (1966), 334-338.
7) T. Kato, Remarks on pseudo-resolvents and infinitesimal generators of semigroups, Proc. Japan Acad., 35 (1959), 467-468.
8) T. Kato, Perturbation theory for linear operators, Die Grundlehren der math. Wissenschaften, 132, Springer-Verlag, Berlin and New York, 1966; 2nd ed., 1976.
9) T. Kato, Nonlinear semigroups and evolution equations, J. Math. Soc. Japan, 19 (1967), 508-520.
10) T. Kato, Schrödinger operators with singular potentials, Israel J. Math., 13 (1972), 135-148.
11) T. Kato, Singular perturbation and semigroup theory, Lecture Notes in Math., 565, Springer-Verlag, Berlin and New York, 1976, 104-112.
12) S. T. Kuroda, Spectral theory II, Iwanami-Shoten, Tokyo, 1979 (in Japanese).
13) G. Lumer and R. S. Phillips, Dissipative operators in a Banach space, Pacific J. Math., 11 (1961), 679-698.
14) E. Nelson, Feynman integrals and the Schrödinger equation, J. Mathematical Phys., 5 (1964), 332-343.
15) N. Okazawa, A perturbation theorem for linear contraction semigroups on reflexive Banach spaces, Proc. Japan Acad., 47 (1971), suppl. II, 947-949.
16) N. Okazawa, Perturbations of linear m-accretive operators, Proc. Amer. Math. Soc., 37 (1973), 169-174.
17) N. Okazawa, Remarks on linear m-accretive operators in a Hilbert space, J. Math. Soc. Japan, 27 (1975), 160-165.
18) N. Okazawa, Singular perturbations of m-accretive operators, J. Math. Soc. Japan, 32 (1980), 19-44.
19) M. Reed and B. Simon, Methods of modern mathematical physics, vol. II, Fourier analysis, selfadjointness, Academic Press, New York, 1975.
20) H. Sohr, Störungskriterien im reflexiven Banachraum, Math. Ann., 233 (1978), 75-87.
21) H. Sohr, Über die Selbstadjungiertheit von Schrödinger-Operatoren, Math. Z., 160 (1978), 255-261.
22) H. Tanabe, Equations of evolution, Monographs and Studies in Math., 6, Pitman, London, 1979.
23) R. Wüst, Generalization of Rellich's theorem on perturbation of (essentially) selfadjoint operators, Math. Z., 119 (1971), 276-280.
24) K. Yosida, Functional analysis, Die Grundlehren der math. Wissenschaften, 123, Springer-Verlag, Berlin and New York, 1965; 5th ed., 1978.
Right : [1] H. Behncke and H. Focke, Stability of deficiency indices, Proc. Roy. Soc. Edinburgh, Sect. A, 78 (1977), 119-127.
[2] P. R. Chernoff, Perturbations of dissipative operators with relative bound one, Proc. Amer. Math. Soc., 33 (1972), 72-74.
[3] W. N. Everitt and M. Giertz, Inequalities and separation for Schrödinger type operators in L2(Rn), Proc. Roy. Soc. Edinburgh, Sect. A, 79 (1977), 257-265.
[4] W. G. Faris and R. B. Lavine, Commutators and selfadjointness of Hamiltonian operators, Comm. Math. Phys., 35 (1974), 39-48.
[5] S. Goldberg, Unbounded linear operators, Theory and applications, Series in Higher Math., McGraw-Hill, New York, 1966.
[6] K. Gustafson, A perturbation lemma, Bull. Amer. Math. Soc., 72 (1966), 334-338.
[7] T. Kato, Remarks on pseudo-resolvents and infinitesimal generators of semigroups, Proc. Japan Acad., 35 (1959), 467-468.
[8] T. Kato, Perturbation theory for linear operators, Die Grundlehren der math. Wissenschaften, 132, Springer-Verlag, Berlin and New York, 1966; 2nd ed., 1976.
[9] T. Kato, Nonlinear semigroups and evolution equations, J. Math. Soc. Japan, 19 (1967), 508-520.
[10] T. Kato, Schrödinger operators with singular potentials, Israel J. Math., 13 (1972), 135-148.
[11] T. Kato, Singular perturbation and semigroup theory, Lecture Notes in Math., 565, Springer-Verlag, Berlin and New York, 1976, 104-112.
[12] S. T. Kuroda, Spectral theory II, Iwanami-Shoten, Tokyo, 1979 (in Japanese).
[13] G. Lumer and R. S. Phillips, Dissipative operators in a Banach space, Pacific J. Math., 11 (1961), 679-698.
[14] E. Nelson, Feynman integrals and the Schrödinger equation, J. Mathematical Phys., 5 (1964), 332-343.
[15] N. Okazawa, A perturbation theorem for linear contraction semigroups on reflexive Banach spaces, Proc. Japan Acad., 47 (1971), suppl. II, 947-949.
[16] N. Okazawa, Perturbations of linear m-accretive operators, Proc. Amer. Math. Soc., 37 (1973), 169-174.
[17] N. Okazawa, Remarks on linear m-accretive operators in a Hilbert space, J. Math. Soc. Japan, 27 (1975), 160-165.
[18] N. Okazawa, Singular perturbations of m-accretive operators, J. Math. Soc. Japan, 32 (1980), 19-44.
[19] M. Reed and B. Simon, Methods of modern mathematical physics, vol. II, Fourier analysis, selfadjointness, Academic Press, New York, 1975.
[20] H. Sohr, Störungskriterien im reflexiven Banachraum, Math. Ann., 233 (1978), 75-87.
[21] H. Sohr, Über die Selbstadjungiertheit von Schrödinger-Operatoren, Math. Z., 160 (1978), 255-261.
[22] H. Tanabe, Equations of evolution, Monographs and Studies in Math., 6, Pitman, London, 1979.
[23] R. Wüst, Generalization of Rellich's theorem on perturbation of (essentially) selfadjoint operators, Math. Z., 119 (1971), 276-280.
[24] K. Yosida, Functional analysis, Die Grundlehren der math. Wissenschaften, 123, Springer-Verlag, Berlin and New York, 1965; 5th ed., 1978.
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