| Title:
|
Generating real maps on a biordered set (English) |
| Author:
|
Martinon, Antonio |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
32 |
| Issue:
|
2 |
| Year:
|
1991 |
| Pages:
|
265-272 |
| . |
| Category:
|
math |
| . |
| Summary:
|
Several authors have defined operational quantities derived from the norm of an operator between Banach spaces. This situation is generalized in this paper and we present a general framework in which we derivate several maps $X\rightarrow \Bbb R$ from an initial one $X\rightarrow \Bbb R$, where $X$ is a set endowed with two orders, $\leq $ and $\leq ^{\ast }$, related by certain conditions. We obtain only three different derivated maps, if the initial map is bounded and monotone. (English) |
| Keyword:
|
derivated map |
| Keyword:
|
biordered set |
| Keyword:
|
admissible order |
| MSC:
|
06A06 |
| MSC:
|
06A10 |
| MSC:
|
47A30 |
| MSC:
|
47A53 |
| idZBL:
|
Zbl 0757.47013 |
| idMR:
|
MR1137787 |
| . |
| Date available:
|
2009-01-08T17:43:53Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/116964 |
| . |
| Reference:
|
[BG] Banas J., Goebel K.: Measures of Noncompactness in Banach Spaces.Marcel Dekker, Lecture Notes in Pure and Applied Math., vol.60; New York, Basel, 1980. Zbl 0441.47056, MR 0591679 |
| Reference:
|
[BO] Bourbaki N.: Éléments de Mathématique. Topologie Générale.Hermann, Paris, 1971. Zbl 1107.54001, MR 0358652 |
| Reference:
|
[FA] Fajnshtejn A.S.: On measures of noncompactness of linear operators and analogs of the minimal modulus for semi-Fredholm operators (in Russian).Spektr. Teor. Oper. 6 (1985), 182-195 Zbl 634 #47010. |
| Reference:
|
[GM1] Gonzalez M., Martinon A.: Operational quantities and operator ideals.Actas XIV Jornadas Hispano-Lusas Mat. (1989), Univ. La Laguna, vol. I, 1990, 383-387. MR 1112904 |
| Reference:
|
[GM2] Gonzalez M., Martinon A.: Operational quantities derived from the norm and measures of noncompactness.Proc. Royal Irish Acad., to appear. MR 1173159 |
| Reference:
|
[GM3] Gonzalez M., Martinon A.: A generalization of semi-Fredholm operators.1990, preprint. |
| Reference:
|
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| Reference:
|
[MA1] Martinon A.: Generating operational quantities in Fredholm theory.Actas XIV Jornadas Hispano-Lusas Mat. (1989), Univ. La Laguna, vol. I, 1990, 449-453. MR 1112916 |
| Reference:
|
[MA2] Martinon A.: Cantidades operacionales en Teoría de Fredholm (Tesis).Univ. La Laguna, 1989. MR 1067932 |
| Reference:
|
[PI] Pietsch A.: Operator Ideals.North-Holland; Amsterdam, New York, Oxford, 1980. Zbl 1012.47001, MR 0582655 |
| Reference:
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| Reference:
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| Reference:
|
[TY] Tylli H.-O.: On the asymptotic behaviour of some quantities related to semi-Fredholm operators.J. London Math. Soc. (2) 31 (1985), 340-348. Zbl 0582.47004, MR 0809955 |
| Reference:
|
[WE] Weis L.: Über strikt singulare und strikt cosingulare Operatoren in Banachräumen (Dissertation).Univ. Bonn, 1974. |
| Reference:
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| . |
