Title:
|
On solvability of nonlinear operator equations and eigenvalues of homogeneous operators (English) |
Author:
|
Burýšková, Věra |
Author:
|
Burýšek, Slavomír |
Language:
|
English |
Journal:
|
Mathematica Bohemica |
ISSN:
|
0862-7959 (print) |
ISSN:
|
2464-7136 (online) |
Volume:
|
121 |
Issue:
|
3 |
Year:
|
1996 |
Pages:
|
301-314 |
Summary lang:
|
English |
. |
Category:
|
math |
. |
Summary:
|
Notions as the numerical range $W(S,T)$ and the spectrum $\s(S,T)$ of couple $(S,T)$ of homogeneous operators on a Banach space are used to derive theorems on solvability of the equation $Sx-lTx=y.$ Conditions for the existence of eigenvalues of the couple $(S,T)$ are given. (English) |
Keyword:
|
Banach and Hilbert space |
Keyword:
|
homogeneous operator |
Keyword:
|
polynomial operator |
Keyword:
|
symmetric operator |
Keyword:
|
monotone operator |
Keyword:
|
numerical range |
Keyword:
|
spectrum |
Keyword:
|
eigenvalue |
MSC:
|
47H15 |
MSC:
|
47J05 |
idZBL:
|
Zbl 0863.47045 |
idMR:
|
MR1419884 |
DOI:
|
10.21136/MB.1996.125984 |
. |
Date available:
|
2009-09-24T21:20:04Z |
Last updated:
|
2020-07-29 |
Stable URL:
|
http://hdl.handle.net/10338.dmlcz/125984 |
. |
Reference:
|
[1] F. Bonsall B. E. Cain H. Schneider: The numerical range of continuous mapping of a normed space.Aequationes Math. 2 (1968), 86-93. MR 0232226 |
Reference:
|
[2] F. E. Browder: Problemes non-lineaires.Univ. Montreal Press, 1966. Zbl 0153.17302 |
Reference:
|
[3] V. Burýšková: Definition und grudlegende Eigenschaften des nichtlinearen adjungierten Operators.Časopis Pěst. Mat. 103 (1978), 186-201. MR 0477929 |
Reference:
|
[4] V. Burýšková: Adjoint nonlinear opeгators.Dissertation, Praha, 1977. (In Czech.) |
Reference:
|
[5] S. Burýšek: Some remarks on polynomial operators.Comment. Math. Univ. Carolin. 10,2 (1969), 285-306. MR 0251560 |
Reference:
|
[6] S. Burýšek: On spectra of nonlinear operators.Comment. Math. Univ. Carolin. 11,4 (1970), 727-743. MR 0288639 |
Reference:
|
[7] S. Burýšek V. Burýšková: Small solutions of a nonlineaг operator equation.Acta Polytech. Práce ČVUT Praze Ser. IV Tech. Teoret. 15 (1982), No. 1, 51-54. MR 0910347 |
Reference:
|
[8] S. Burýšek V. Burýšková: Some results from theory of homogeneous operators.CTU Seminar, 1994. |
Reference:
|
[9] V. Burýšková S. Burýšek: On the convexity of the numeгical range of homogeneous operatoгs.Acta Polytech. Práce ČVUT Praze Ser. IV Tech. Teoret. 34 (1994), No. 2, 25-33. |
Reference:
|
[10] V. Burýšková: Některé výsledky z teorie nelineárních operátorů a operátorových rovnic.Habilitation Thesis, Praha, 1994. (In Czech.) |
Reference:
|
[11] S. Burýšek V. Burýšková: On the aproximative spectrum of the couple of homogeneous operators.Acta Polytech. Práce ČVUT Praze Ser. IV Tech. Teoret. 35 (1995), No. 1, 5-16. |
Reference:
|
[12] G. Conti E. DePascale: The numerical range in the nonlineaг case.Boll. Un. Mat. Ital. B(5), 15 (1978), 210-216. MR 0493572 |
Reference:
|
[13] J. A. Canavati: A theory of numerical range for nonlinear operators.J. Funct. Anal. 33 (1979), 231-258. Zbl 0445.47045, MR 0549114, 10.1016/0022-1236(79)90067-3 |
Reference:
|
[14] M. Furi A. Vignoli: Spectrum of nonlinear maps and bifuгcations in the nondifferentiable case.Ann. Math. Pura Appl. (4) 113 (1977), 265-285. MR 0493558 |
Reference:
|
[15] S. K. Kyong Y. Youngoh: On the numerical range for nonlinear operators.Bull. Korean Math. Soc. 21 (1984), No. 2, 119-126. MR 0768468 |
Reference:
|
[16] J. Prüss: A characterization of uniform convexity and applications to accretive operators.Hiroshima Math. J., 11 (1981), No. 2, 229-234. MR 0620534, 10.32917/hmj/1206134097 |
Reference:
|
[17] A. Rhodius: Deг numeгische Wertebereich für nicht netwendig lineare Abbildungen in lokalkonvexen Räumen.Math. Nachr. 72 (1976), 169-180. MR 0410501, 10.1002/mana.19760720115 |
Reference:
|
[18] A. E. Taylor: Úvod do funkcionální analýzy.Academia, Praha, 1973. |
Reference:
|
[19] M. M. Vajnberg: Variational Method and Method of Monotone Operators in the Theory of Nonlinear Equations.Moskva, 1972. (In Russian.) |
Reference:
|
[20] Verma U. Ram: Numerical range and related nonlinear functional equations.Czechoslovak Math. J. 42 (117) (1992), No. 3, 503-513. Zbl 0781.47048, MR 1179314 |
Reference:
|
[21] K. Yosida: Functional Analysis.Spгinger-Verlag, Berlin, 1965. Zbl 0126.11504 |
Reference:
|
[22] E. H. Zarantonello: The closure of the numerical range contains the spectrum.Pacific J. Math. 22 (1967), No. 3, 575-595. Zbl 0152.34602, MR 0229079, 10.2140/pjm.1967.22.575 |
. |