119
Views
4
CrossRef citations to date
0
Altmetric
Original Articles

Coperturbation function and lower semi-Browder multivalued linear operators

, &
Pages 494-516 | Received 26 Nov 2011, Accepted 04 May 2012, Published online: 18 Jun 2012

References

  • Agarwal , RP , Meehan , M and O'Regan , D . 2001 . Fixed Point Theory and Applications , Cambridge : University Press .
  • Alvarez , T . 1998 . Perturbation and coperturbation functions characterising semi-Fredholm type operators , 41 โ€“ 46 . Math. Proc. Royal Irish Acad. 98 A .
  • Alvarez , T . 2004 . Perturbation theorems for upper and lower semi-Fredholm linear relations . Publ. Math. Debrecen. , 65 : 179 โ€“ 191 .
  • Alvarez , T , Cross , RW and Wilcox , D . 2001 . Multivalued Fredholm type operators with abstract generalised inverses . J. Math. Anal. Appl. , 261 : 403 โ€“ 417 .
  • Alvarez , T , Cross , RW and Wilcox , D . 2002 . Quantities related to upper and lower semi-Fredholm type linear relations . Bull. Aus. Math. Soc. , 66 : 275 โ€“ 289 .
  • Alvarez , T and Wilcox , D . 2007 . Perturbation theory of multivalued Atkinson operators in normed spaces . Bull. Aus. Math. Soc. , 76 : 195 โ€“ 204 .
  • Coddington , EA . 1971 . โ€œ Multivalued Operators and Boundary Value Problems โ€ . In Lecture Notes in Mathematics , Vol. 183 , Berlin : Springer-Verlag .
  • Coddington , EA and Dijksma , A . 1976 . Selfadjoint subspaces and eigenfunction expansions for ordinary differential subspaces . J. Differ. Eqns. , 20 : 473 โ€“ 526 .
  • Cross , RW . 1988 . Properties of some norm related functions of unbounded linear operators . Math. Z. , 199 : 285 โ€“ 302 .
  • Cross , RW . 1998 . Multivalued Linear Operators , New York : Marcel Dekker .
  • Cross , RW and Labuschagne , LE . 1992 . Characterizations of operators of lower semi-Fredholm type in normed spaces . Quaestiones Math. , 15 : 151 โ€“ 173 .
  • Dijksma , A , EL Sabbah , A and de Snoo , HSV . 1990 . Self-adjoint extensions of regular canonical systems with Stieltjes boundary conditions . J. Math. Anal. Appl. , 152 : 546 โ€“ 583 .
  • Fakhfakh , F and Mnif , M . 2008 . Perturbation of semi-Browder operators and stability of Browder's essential defect and approximate point spectrum . J. Math. Anal. Appl. , 347 : 235 โ€“ 242 .
  • Fakhfakh , F and Mnif , M . 2009 . Browder and semi-browder operators and perturbation function . Extrac. Math. , 24 : 219 โ€“ 241 .
  • Fakhfakh , F and Mnif , M . 2011 . Perturbation theory of lower semi-Browder multivalued linear operators . Publ. Math. Debrecen. , 78 : 595 โ€“ 606 .
  • Favini , A and Yagi , A . 1993 . Multivalued linear operators and degenerate evolution equations . Ann. Mat. Pura. Appl. , 163 : 353 โ€“ 384 .
  • Gohberg , IC , Goldberg , S and Kaashoek , MA . 1990 . โ€œ Classes of Operators โ€ . In Vol. I, Operator Theory: Advances and Applications , Vol. 49 , Basel-Boston-Berlin : Birkhรคuser-Verlag .
  • Goldman , MA and Kra[cbreve]kovskii , SN . 1975 . Behavior of the space of zero elements with finite-dimensional salient on the Riesz kernel under perturbations of the operator . Dokl. Akad. Nauk SSSR , 221 : 532 โ€“ 534 [English transl., Soviet Math. Dokl. 16, (1975), 370โ€“373] .
  • Gorniewicz , L . 1999 . Topological Fixed Point Theory of Multivalued Mappings , Dordrecht : Kluwer .
  • Grabiner , S . 1978 . Ascent, descent, and compact perturbations . Proc. Am. Math. Soc. , 71 : 79 โ€“ 80 .
  • Gromov , M . 1986 . Partial Differential Relations , Berlin : Springer-Verlag .
  • Jaftha , JJ . 2006 . The conjugate of a product of linear relations . Comment. Math. Univ. Carolin. , 47 : 265 โ€“ 273 .
  • Labuschagne , LE . 1991 . Characterisations of partially continuous strictly cosingular and ฮฆ_ type operators . Glasgow Math. J. , 33 : 203 โ€“ 212 .
  • Muresan , M . 1994 . On a boundary value problem for quasi-linear differential inclusions of evolution . Collect. Math. , 45 : 165 โ€“ 175 .
  • Rako[cbreve]eviฤ‡ , V . 1995 . Semi-Fredholm operators with finite ascent or descent and perturbations . Proc. Am. Math. Soc. , 123 : 3823 โ€“ 3825 .
  • Rako[cbreve]eviฤ‡ , V . 1997 . Semi-Browder operators and perturbations . Studia Math. , 122 : 131 โ€“ 137 .
  • Roman-Flores , H , Flores-Franulic , A , Rojas-Medar , MA and Bassanezi , RC . 1998 . Stability of the fixed points set of fuzzy contractions . Appl. Math. Lett. , 11 : 33 โ€“ 37 .
  • Sandovici , A and de Snoo , H . 2009 . An index formula for the product of linear relations . Linear Alg. Appl. , 431 : 2160 โ€“ 2171 .
  • Sandovici , A , de Snoo , H and Winkler , H . 2007 . Ascent, descent, nullity, defect and related notions for linear relations in linear spaces . Linear Alg. Appl. , 423 : 456 โ€“ 497 .
  • Schechter , M . 2002 . โ€œ Principles of Functional Analysis โ€ . In Graduate Studies in Mathematics , 2nd , Vol. 36 , Providence , , RI : American Mathematical Society .
  • von Neumann , J . 1950 . โ€œ Functional Operators, II. The Geometry of Orthogonal Spaces โ€ . In Annals of Mathematical Studies , Vol. 22 , Princeton , , NJ : Princeton University Press .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.