Singular perturbations of m-accretive operators

Noboru OKAZAWA

doi:10.2969/jmsj/03210019

Noboru OKAZAWA

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1980 Volume 32 Issue 1 Pages 19-44

DOI https://doi.org/10.2969/jmsj/03210019

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Published: 1980 Received: March 01, 1978 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) M.S. Baouendi and C. Goulaouic, Régularité et théorie spectrale pour une classe d'opérateurs elliptiques dégénérés, Arch. Rational Mech. Anal., 34 (1969), 361-379.
2) V. Barbu, Nonlinear Semigroups and Differential Equations in Banach Spaces, Noordhoff International Publ., Leyden, The Netherlands, 1976.
3) Ph. Benilan, Une remarque sur la convergence des semigroupes nonlinéaires, C.R. Acad. Sci. Paris, 272 (1971), 1182-1184.
4) P.R. Chernoff, Note on product formulas for operator semigroups, J. Functional Analysis, 2 (1968), 238-242.
5) P.R. Chernoff, Perturbations of dissipative operators with relative bound one, Proc. Amer. Math. Soc., 33 (1972), 72-74.
6) W.G. Fans and R.B. Lavine, Commutators and selfadjointness of Hamiltonian operators, Comm. Math. Phys., 35 (1974), 39-48.
7) K. Gustafson, A perturbation lemma, Bull. Amer. Math. Soc., 72 (1966), 334-338.
8) T. Kato, Remarks on pseudo-resolvents and infinitesimal generators of semigroups, Proc. Japan Acad., 35 (1959), 467-468.
9) T. Kato, Nonlinear semigroups and evolution equations, J. Math. Soc. Japan, 19 (1967), 508-520.
10) T. Kato, Accretive operators and nonlinear evolution equations in Banach spaces, Nonlinear Functional Analysis, Proc. Symp. Pure Math., Amer. Math. Soc., 18, Part I (1970), 138-161.
11) T. Kato, Perturbation Theory for Linear Operators, 2nd ed., Die Grundlehren der math. Wissenschaften, Band 132, Springer-Verlag, Berlin and New York, 1976.
12) Y. Konishi, A remark on perturbation of m-accretive operators in Banach space, Proc. Japan Acad., 47 (1971), 452-455.
13) G. Lumer and R.S. Phillips, Dissipative operators in a Banach space, Pacific J. Math., 11 (1961), 679-698.
14) R.H. Martin, Jr., Nonliner Operators and Differential Equations in Banach Spaces, A Wiley-Interscience Publ., New York, 1976.
15) I. Miyadera, Nonlinear Semigroups, Kinokuniya, Tokyo, 1977, (Japanese).
16) N.Okazawa, Two perturbation theorems for contraction semigroups in a Hilbert space, Proc. Japan Acad., 45 (1969) 850-853.
17) N. Okazawa, A perturbation theorem for linear contraction semigroups on reflexive Banach spaces, Proc. Japan Acad., 47 (1971), 947-949.
18) N. Okazawa, Perturbations of linear m-accretive operators, Proc. Amer. Math. Soc., 37 (1973), 169-174.
19) N. Okazawa, Remarks on linear m-accretive operators in a Hilbert space, J. Math. Soc. Japan, 27 (1975), 160-165.
20) N. Okazawa, Approximation of linear m-accretive operators in a Hilbert space, Osaka J. Math., 14 (1977), 85-94.
21) N. Shimakura, General boundary value problems for elliptic operators which degenerate at the boundary, Kôkyûroku, Res. Inst. Math. Sci., Kyoto Univ., 88 (1970), 1-20 (Japanese).
22) A. Yoshikawa, On Perturbation of closed operators in a Banach space, J. Fac. Sci. Hokkaido Univ., 22 (1972), 50-61.
23) K. Yosida, Functional Analysis, 3rd ed., Die Grundlehren der math. Wissenschaften, Band 123, Springer-Verlag, Berlin and New York, 1971.

Right : [1] M. S. Baouendi and C. Goulaouic, Régularité et théorie spectrale pour une classe d'opérateurs elliptiques dégénérés, Arch. Rational Mech. Anal., 34 (1969), 361-379.
[2] V. Barbu, Nonlinear Semigroups and Differential Equations in Banach Spaces, Noordhoff International Publ., Leyden, The Netherlands, 1976.
[3] Ph. Benilan, Une remarque sur la convergence des semigroupes nonlinéaires, C. R. Acad. Sci. Paris, 272 (1971), 1182-1184.
[4] P. R. Chernoff, Note on product formulas for operator semigroups, J. Functional Analysis, 2 (1968), 238-242.
[5] P. R. Chernoff, Perturbations of dissipative operators with relative bound one, Proc. Amer. Math. Soc., 33 (1972), 72-74.
[6] W. G. Fans and R. B. Lavine, Commutators and selfadjointness of Hamiltonian operators, Comm. Math. Phys., 35 (1974), 39-48.
[7] K. Gustafson, A perturbation lemma, Bull. Amer. Math. Soc., 72 (1966), 334-338.
[8] T. Kato, Remarks on pseudo-resolvents and infinitesimal generators of semigroups, Proc. Japan Acad., 35 (1959), 467-468.
[9] T. Kato, Nonlinear semigroups and evolution equations, J. Math. Soc. Japan, 19 (1967), 508-520.
[10] T. Kato, Accretive operators and nonlinear evolution equations in Banach spaces, Nonlinear Functional Analysis, Proc. Symp. Pure Math., Amer. Math. Soc., 18, Part I (1970), 138-161.
[11] T. Kato, Perturbation Theory for Linear Operators, 2nd ed., Die Grundlehren der math. Wissenschaften, Band 132, Springer-Verlag, Berlin and New York, 1976.
[12] Y. Konishi, A remark on perturbation of m-accretive operators in Banach space, Proc. Japan Acad., 47 (1971), 452-455.
[13] G. Lumer and R. S. Phillips, Dissipative operators in a Banach space, Pacific J. Math., 11 (1961), 679-698.
[14] R. H. Martin, Jr., Nonliner Operators and Differential Equations in Banach Spaces, A Wiley-Interscience Publ., New York, 1976.
[15] I. Miyadera, Nonlinear Semigroups, Kinokuniya, Tokyo, 1977, (Japanese).
[16] N.Okazawa, Two perturbation theorems for contraction semigroups in a Hilbert space, Proc. Japan Acad., 45 (1969) 850-853.
[17] N. Okazawa, A perturbation theorem for linear contraction semigroups on reflexive Banach spaces, Proc. Japan Acad., 47 (1971), 947-949.
[18] N. Okazawa, Perturbations of linear m-accretive operators, Proc. Amer. Math. Soc., 37 (1973), 169-174.
[19] N. Okazawa, Remarks on linear m-accretive operators in a Hilbert space, J. Math. Soc. Japan, 27 (1975), 160-165.
[20] N. Okazawa, Approximation of linear m-accretive operators in a Hilbert space, Osaka J. Math., 14 (1977), 85-94.
[21] N. Shimakura, General boundary value problems for elliptic operators which degenerate at the boundary, Kôkyûroku, Res. Inst. Math. Sci., Kyoto Univ., 88 (1970), 1-20 (Japanese).
[22] A. Yoshikawa, On Perturbation of closed operators in a Banach space, J. Fac. Sci. Hokkaido Univ., 22 (1972), 50-61.
[23] K. Yosida, Functional Analysis, 3rd ed., Die Grundlehren der math. Wissenschaften, Band 123, Springer-Verlag, Berlin and New York, 1971.

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