| Title:
|
Alcune osservazioni sul rango numerico per operatori non lineari (Italian) |
| Title:
|
Some remarks on numerical ranges for nonlinear operators (English) |
| Author:
|
Appell, Jürgen |
| Author:
|
Conti, G. |
| Author:
|
Santucci, P. |
| Language:
|
Italian |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
124 |
| Issue:
|
2 |
| Year:
|
1999 |
| Pages:
|
185-192 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We discuss some numerical ranges for Lipschitz continuous nonlinear operators and their relations to spectral sets. In particular, we show that the spectrum defined by Kachurovskij (1969) for Lipschitz continuous operators is contained in the so-called polynomial hull of the numerical range introduced by Rhodius (1984). (English) |
| Keyword:
|
nonlinear operator |
| Keyword:
|
Lipschitz continuity |
| Keyword:
|
spectrum |
| Keyword:
|
numerical range |
| Keyword:
|
convex hull |
| Keyword:
|
polynomial hull |
| MSC:
|
15A60 |
| MSC:
|
47A12 |
| MSC:
|
47H09 |
| MSC:
|
47H12 |
| MSC:
|
47H17 |
| MSC:
|
47H99 |
| MSC:
|
47J10 |
| MSC:
|
47J25 |
| MSC:
|
47J99 |
| MSC:
|
65F99 |
| idZBL:
|
Zbl 0940.47052 |
| idMR:
|
MR1780691 |
| DOI:
|
10.21136/MB.1999.126249 |
| . |
| Date available:
|
2009-09-24T21:36:59Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/126249 |
| . |
| Reference:
|
[1] Appell J., De Pascale E., Vignoli A.: A comparison of different spectra for nonlinear operators.To appear. Zbl 0956.47035 |
| Reference:
|
[2] Appell J., Dörfner M.: Some spectral theory for nonlinear operators.Nonlinear Anal., Theory Methods Appl. 28 (1997), no. 12, 1955-1976. Zbl 0876.47042, MR 1436365, 10.1016/S0362-546X(96)00040-5 |
| Reference:
|
[3] Bonsall F. F., Duncan J.: Numerical Ranges of Operators on Normed Spaces and of Elements of Normed Algebras.Cambridge Univ. Press, Cambridge, 1971. Zbl 0207.44802, MR 0288583 |
| Reference:
|
[4] Bonsall F. F., Duncan J.: Numerical Ranges II.Cambridge Univ.Press, Cambridge, 1973. Zbl 0262.47001, MR 0442682 |
| Reference:
|
[5] Canavati J.: A theory of numerical range for nonlinear operators.J. Fund. Anal. 33 (1979), 231-258. Zbl 0445.47045, MR 0549114, 10.1016/0022-1236(79)90067-3 |
| Reference:
|
[6] Conti G., De Pascale E.: The numerical range in the nonlinear case.Boll. Unione Mat. Ital. 15-B (1978), 210-216. Zbl 0386.47042, MR 0493572 |
| Reference:
|
[7] Deimling K.: Nonlinear Functional Analysis.Springer, Berlin, 1985. Zbl 0559.47040, MR 0787404 |
| Reference:
|
[8] Diestel J.: Geometry of Banach Spaces-Selected Topics.Springer, Berlin, 1975. Zbl 0307.46009, MR 0461094 |
| Reference:
|
[9] Dörfner M.: Beiträge zur Spektraltheorie nichtlinearer Operatoren.Ph.D. thesis, 1997. |
| Reference:
|
[10] Feng W.: A new spectral theory for nonlinear operators and its applications.Abstr. Appl. Anal. 2 (1997), 163-183. Zbl 0952.47047, MR 1604177, 10.1155/S1085337597000328 |
| Reference:
|
[11] Furi M., Martelli M., Vignoli A.: Contributions to the spectral theory for nonlinear operators in Banach spaces.Annali Mat. Pura Appl. 118 (1978), 229-294. Zbl 0409.47043, MR 0533609 |
| Reference:
|
[12] Furi M., Martelli M., Vignoli A.: On the solvability of nonlinear operator equations in normed spaces.Annali Mat. Pura Appl. 128 (1980), 321-343. Zbl 0456.47051, MR 0591562 |
| Reference:
|
[13] Gustafson K. E., Rao D. K. M.: Numerical Range.Springer, Berlin, 1997. MR 1417493 |
| Reference:
|
[14] Kachurovskij R. L: Regular points, spectrum and eigenfunctions of nonlinear operators.Dokl. Akad. Nauk SSSR 188 (1969), 274-277. (In Russian, Engl.transl. Soviet Math. Dokl. 10 (1969), 1101-1105.) Zbl 0197.40402, MR 0251599 |
| Reference:
|
[15] Lumer G.: Semi-inner product spaces.Transl. Amer. Math. Soc. 100 (1961), 29-43. Zbl 0102.32701, MR 0133024, 10.1090/S0002-9947-1961-0133024-2 |
| Reference:
|
[16] Maddox I. J., Wickstead A. W.: The spectrum of uniformly Lipschitz mappings.Proc. Royal Irish Acad. 89-A (1989), 101-114. Zbl 0661.47048, MR 1021228 |
| Reference:
|
[17] Neuberger J. W.: Existence of a spectrum for nonlinear transformations.Pacific J. Math. 31 (1969), 157-159. Zbl 0182.47203, MR 0259696, 10.2140/pjm.1969.31.157 |
| Reference:
|
[18] Pietschmann F., Rhodius A.: The numerical ranges and the smooth points of the unit sphere.Act. Sci. Math. 55 (1989), 377-379. Zbl 0697.47003, MR 1033610 |
| Reference:
|
[19] Rhodius A.: Der numerische Wertebereich für nicht notwendig lineare Abbildungen.Math. Nachr. 72 (1976), 169-180. Zbl 0297.47059, MR 0410501, 10.1002/mana.19760720115 |
| Reference:
|
[20] Rhodius A.: Der numerische Wertebereich und die Lösbarkeit linearer und nichtlinearer Gleichungen.Math. Nachr. 79 (1977), 343-360. MR 0637086, 10.1002/mana.19770790137 |
| Reference:
|
[21] Rhodius A.: Über numerische Wertebereiche und Spektralwertabschätzungen.Acta Sci. Math. 47 (1984), 465-470. Zbl 0575.47005, MR 0783322 |
| Reference:
|
[22] Verma R. U.: Approximation-solvability and numerical ranges in Banach spaces.Panam. Math. J. 1 (1992), 49-56. MR 1116245 |
| Reference:
|
[23] Verma R. U.: The numerical range of nonlinear Banach space operators.Acta Math. Hung. 63 (1994), 305-312. Zbl 0796.47051, MR 1261473, 10.1007/BF01874455 |
| Reference:
|
[24] Williams J. P.: Spectra of products and numerical ranges.J. Math. Anal. Appl. 11 (1967), 214-220. Zbl 0143.36703, MR 0203491, 10.1016/0022-247X(67)90146-1 |
| Reference:
|
[25] Zarantonello E. H.: The numerical range contains the spectrum.Pacific J. Math. 22 (1967), 575-595. Zbl 0152.34602, MR 0229079, 10.2140/pjm.1967.22.575 |
| Reference:
|
[26] Zeidler E.: Nonlinear Functional Anaiysis and its Applications II/B: Nonlinear Monotone Operators.Springer, Berlin, 1990. MR 1033498 |
| . |
