Skip to main content Accessibility help
×
Home

Quantities related to upper and lower semi-Fredholm type linear relations

  • Teresa Alvarez (a1), Ronald Cross (a2) and Diane Wilcox (a3)

Extract

Certain norm related functions of linear operators are considered in the very general setting of linear relations in normed spaces. These are shown to be closely related to the theory of strictly singular, strictly cosingular, F+ and F linear relations. Applications to perturbation theory follow.

    • Send article to Kindle

      To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

      Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

      Find out more about the Kindle Personal Document Service.

      Quantities related to upper and lower semi-Fredholm type linear relations
      Available formats
      ×

      Send article to Dropbox

      To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

      Quantities related to upper and lower semi-Fredholm type linear relations
      Available formats
      ×

      Send article to Google Drive

      To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

      Quantities related to upper and lower semi-Fredholm type linear relations
      Available formats
      ×

Copyright

References

Hide All
[1]Arens, R., ‘Operational calculus of linear relations’, Pacific J. Math. 11 (1961), 923.
[2]Aubin, J.P. and Cellina, A., Differential inclusions. Set valued maps and viability theory. (Springer-Verlag, Berlin, New York, 1984).
[3]Aubin, J.P. and Frankowska, H., Set Valued analysis (Birkhauser, Boston, 1990).
[4]Clarke, F.H., Optimization and nonsmooth analysis, Canadian Mathematical Society Series of Monographs and Advanced Texts (J. Wiley and Sons, Toronto, 1983).
[5]Coddington, E.A., Multivalued operators and boundary value problems, Lecturs Notes in Math. 183 (Springler-Verlag, Berlin, 1971).
[6]Coddington, E.A. and Dijksma, A., ‘Selfadjoint subspaces and eigenfunction expansions for ordinary differential subspaces’, J. Differential Equations 20 (1976), 473526.
[7]Cross, R.W., ‘Properties of some norm related functions of unbounded linear operators’, Math. Z. 199 (1988), 285302.
[8]Cross, R.W., Multivalued linear operators, Monographs and Textbooks in Pure and Applied Mathematics 213 (Marcel Dekker, New York, 1998).
[9]Cross, R.W. and Labuschagne, L.E., ‘Characterisations of operators of lower semi-Fredholm type in normed linear spaces’, quaestiones Math. 15 (1992), 151173.
[10]Dijksma, A., El Sabbah, A. and deSnoo, H.S.V., ‘Selfadjoint extensions of regular canonical systems with Stieltjes boundary conditions’, J. Math. Anal. 152 (1990), 546583.
[11]Fajnshtejn, A.S., ‘On measures of noncompactness of linear operators and anlogoues of the minimal modulus for semi-Fredholm operators’, (Russian), Spektr. Teor. Oper. 6 (1985), 182195.
[12]Favini, A. and Yagi, A., ‘Multivalued linear operators and degenerate evolution equations’, Ann. Mat. Pura. Appl. (4) 163 (1993), 353384.
[13]Gramsch, B., Über analytische Störungen und den Index von Fredholmoperatoren auf (Banachräumen, Dept. Mathematics, Univ. Maryland, 1969).
[14]Goldberg, S., Unbounded linear operators, Theory and Applications (McGraw-Hill, New York, 1966).
[15]González, M. and Martinón, A., ‘Operational quantities derived from the norm and measures of noncompactness’, Proc. Roy. Irish Acad. Sect. A 91 (1991), 6370.
[16]Gromov, M., Partial differential relations (Springer-Verlag, Berlin, 1986).
[17]Kato, T., Perturbation theory for linear operators (Springer-Verlag, Berlin, 1966).
[18]Lebow, A. and Schechter, M., ‘Semigroups of operators and measures of noncompactness’, J. Funct. Anal. 7 (1971), 126.
[19]Martinón, A., Operational quantities in Fredholm theory, (Spanish) (Thesis, Univ. La Laguna, 1989).
[20]Mennicken, R. and Sagraloff, B., ‘Eine Verallgemeinerung des Satzes von abgeschlossenen Werterbereich in lokalkonvexen Räumrn’, Manuscripta Math. 18 (1976), 109146.
[21]von Neumann, J., Functional operators, II. The Geometry of Orthogonal spaces, Annals of Math. Studies 22 (Princeton University Press, Princeton, N.J., 1950).
[22]Pietsch, A., Operators ideals, North-Holland Mathematical Library 20 (North-Holland, Amsterdam, 1980).
[23]Rakočević, V., ‘On one subset of M. Schechter spectrum’, Mat. Vesnik 5 (1981), 389391.
[24]Rakočević, V., ‘Measures of non-strict-singularity of operators’, Mat. Vesnik 35 (1981), 7982.
[25]Schechter, M., ‘Quantities related to strictly singular operators’, Indiana Univ. Math. J. 21 (1972), 10611071.
[26]Sedaev, A.A., ‘The structure of certain linear operators’, (Russian), Mat. Issled. 5 (1970), 166175.
[27]Tylli, H.O., ‘On the asymptotic behaviour of some quantities related to semi-Fredholm operators’, J. London Math. Soc. (2) 31 (1985), 340348.
[28]Weis, L., Über strikt singularë und strikt cosingularë Operatoren in Banachräumen, (Dissertation) (Bonn, 1974).
[29]Weis, L., ‘On perturbations of Fredholm operators in Lp (μ) spaces’, Proc. Amer. Math. Soc. 67 (1977), 287292.
[30]Weis, L., ‘On the computation of some quantities in the theory of Fredholm operatorsRend. Cir. Math. Palermo (2) 5 (1984), 109133.
[31]Zemánek, J., ‘Geometric characteristics of semi-Fredholm operators and their asymptotic behaviour’, Studia Math. 80 (1984), 219234.
[32]Zemánek, J., ‘The semi-Fredholm radius of a linear operator’, Bull. Polish Acad. Sci. Math. 32 (1984), 6776.
[33]Zemánek, J., ‘On the Δ-characteristic of M. Schechter’,in Proceedings of the International Conference,Leipzig,1983 (Teubner, Leipzig, 1984).
MathJax
MathJax is a JavaScript display engine for mathematics. For more information see http://www.mathjax.org.

Quantities related to upper and lower semi-Fredholm type linear relations

  • Teresa Alvarez (a1), Ronald Cross (a2) and Diane Wilcox (a3)

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed