Weakly closed 𝑚-accretive operators

Yamamoto, A.; Okazawa, N.

doi:10.1090/S0002-9939-1977-0467409-9

Weakly closed $m$-accretive operators
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by A. Yamamoto and N. Okazawa

Proc. Amer. Math. Soc. 66 (1977), 284-288

DOI: https://doi.org/10.1090/S0002-9939-1977-0467409-9

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Abstract:

Let A and B be weakly closed, nonlinear m-accretive (single-valued) operators in a reflexive Banach space X, and ${B_n}$ be the Yosida approximation of B. Then the following condition is sufficient for the sum $A + B$ to be also m-accretive: For each $v \in X,\left \| {{B_n}{u_n}} \right \|$ is bounded as n tends to infinity, where ${u_n}$ is defined by the equation ${u_n} + A{u_n} + {B_n}{u_n} = v,n = 1,2, \ldots$. Some related conditions are also provided.

References

H. Brezis, M. G. Crandall, and A. Pazy, Perturbations of nonlinear maximal monotone sets in Banach space, Comm. Pure Appl. Math. 23 (1970), 123–144. MR 257805, DOI 10.1002/cpa.3160230107
V. Barbu, Weak solutions for nonlinear functional equations in Banach spaces, Ann. Mat. Pura Appl. (4) 87 (1970), 87–110. MR 298484, DOI 10.1007/BF02411973
Paul R. Chernoff, Perturbations of dissipative operators with relative bound one, Proc. Amer. Math. Soc. 33 (1972), 72–74. MR 296745, DOI 10.1090/S0002-9939-1972-0296745-X
W. E. Fitzgibbon, Nonlinear perturbation of $m$-accretive operators, Proc. Amer. Math. Soc. 44 (1974), 359–364. MR 343112, DOI 10.1090/S0002-9939-1974-0343112-8
Tosio Kato, Nonlinear semigroups and evolution equations, J. Math. Soc. Japan 19 (1967), 508–520. MR 226230, DOI 10.2969/jmsj/01940508
Tosio Kato, Accretive operators and nonlinear evolution equations in Banach spaces. , Nonlinear Functional Analysis (Proc. Sympos. Pure Math., Vol. XVIII, Part 1, Chicago, Ill., 1968) Amer. Math. Soc., Providence, R.I., 1970, pp. 138–161. MR 0271782
Yoshio Konishi, A remark on perturbation of $m$-accretive operators in Banach space, Proc. Japan Acad. 47 (1971), 452–455. MR 318994
Isao Miyadera, Some remarks on semi-groups of nonlinear operators, Tohoku Math. J. (2) 23 (1971), 245–258. MR 296746, DOI 10.2748/tmj/1178242643
Noboru Okazawa, A perturbation theorem for linear contraction semigroups on reflexive Banach spaces, Proc. Japan Acad. 47 (1971), no. suppl, suppl. II, 947–949. MR 313877, DOI 10.2183/pjab1945.47.SupplementII_{9}47
Noboru Okazawa, Perturbations of linear $m$-accretive operations, Proc. Amer. Math. Soc. 37 (1973), 169–174. MR 313850, DOI 10.1090/S0002-9939-1973-0313850-0
Kôsaku Yosida, Functional analysis, 2nd ed., Die Grundlehren der mathematischen Wissenschaften, Band 123, Springer-Verlag New York, Inc., New York, 1968. MR 0239384, DOI 10.1007/978-3-662-11791-0