Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Operators which have a closed quasi-nilpotent part


Authors: Pietro Aiena, Maria Luisa Colasante and Manuel González
Journal: Proc. Amer. Math. Soc. 130 (2002), 2701-2710
MSC (2000): Primary 47A10, 47A11; Secondary 47A53, 47A55
Published electronically: March 12, 2002
MathSciNet review: 1900878
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We find several conditions for the quasi-nilpotent part of a bounded operator acting on a Banach space to be closed. Most of these conditions are established for semi-Fredholm operators or, more generally, for operators which admit a generalized Kato decomposition. For these operators the property of having a closed quasi-nilpotent part is related to the so-called single valued extension property.


References [Enhancements On Off] (What's this?)

  • 1. P. Aiena, O. Monsalve Operators which do not have the single valued extension property. J. Math. Anal. Appl. 250 (2000), 435-448. MR 2001g:47005
  • 2. P. Aiena, O. Monsalve The single valued extension property and the generalized Kato decomposition property. Acta Sci. Math.(Szeged) 67 (2001), 461-477.
  • 3. F. F. Bonsall, J. Duncan Complete normed algebras. Springer-Verlag, Berlin, 1973. MR 54:11013
  • 4. I. Colojoara, C. Foias Theory of generalized spectral operators. Gordon and Breach, New York, 1968. MR 52:15085
  • 5. N. Dunford Spectral theory II. Resolution of the identity. Pacific J. Math. 2 (1952), 559-614. MR 14:479a
  • 6. N. Dunford Spectral operators. Pacific J. Math. 4 (1954), 321-354. MR 16:142d
  • 7. N. Dunford, J. T. Schwartz Linear operators, Part III. (1971), Wiley, New York. MR 54:1009
  • 8. J. K. Finch The single valued extension property on a Banach space. Pacific. J. Math. 58 (1975), 61-69. MR 51:11181
  • 9. H. Heuser Functional Analysis. (1982), Wiley, New York. MR 83m:46001
  • 10. T. Kato Perturbation theory for nullity, deficiency and other quantities of linear operators. J. Anal. Math. 6 (1958), 261-322. MR 21:6541
  • 11. R. Larsen An introduction to the theory of multipliers. Springer-Verlag, New York, 1979. MR 55:8695
  • 12. K. B. Laursen, Essential spectra through local spectral theory. Proc. Amer. Math. Soc. 125 (1997), 1425-1434. MR 97g:46066
  • 13. K. B. Laursen, M. Mbekhta Closed range multipliers and generalized inverses. Studia Math. 107 (1993), 127-135. MR 94i:47052
  • 14. K. B. Laursen, M. M. Neumann An introduction to local spectral theory. Clarendon Press, Oxford, 2000. MR 2001k:47002
  • 15. M. Mbekhta Généralisation de la décomposition de Kato aux opérateurs paranormaux et spectraux. Glasgow Math. J. 29 (1987), 159-175. MR 88i:47010
  • 16. M. Mbekhta Sur la théorie spectrale locale et limite des nilpotents. Proc. Amer. Math. Soc. 110 (1990), 621-631. MR 91b:47004
  • 17. M. Mbekhta, A. Ouahab Opérateur s-régulier dans un espace de Banach et théorie spectrale. Acta Sci. Math. (Szeged) 59 (1994), 525-543. MR 96a:47018
  • 18. M. Ó Searcóid , T. T. West Continuity of the generalized kernel and range for semi-Fredholm operators. Math. Proc. Camb. Phil. Soc. 105 (1989), 513-522. MR 90d:47017
  • 19. C. Schmoeger On isolated points of the spectrum of a bounded operator. Proc. Amer. Math. Soc. 117 (1993), 715-719. MR 93d:47007
  • 20. P. Vrbová On local spectral properties of operators in Banach spaces. Czechoslovak Math. J. 23 (98) (1973), 483-92. MR 48:898
  • 21. T. T. West A Riesz-Schauder theorem for semi-Fredholm operators. Proc. Roy. Irish. Acad. 87 A (1987), 137-146. MR 89i:47020

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 47A10, 47A11, 47A53, 47A55

Retrieve articles in all journals with MSC (2000): 47A10, 47A11, 47A53, 47A55


Additional Information

Pietro Aiena
Affiliation: Dipartimento di Matematica ed Applicazioni, Facoltà di Ingegneria, Università di Palermo, Viale delle Scienze, I-90128 Palermo, Italy
Email: paiena@mbox.unipa.it

Maria Luisa Colasante
Affiliation: Departamento de Matemáticas, Facultad de Ciencias, Universidad de Los Andes, Merida, Venezuela
Email: marucola@ciens.ula.ve

Manuel González
Affiliation: Departamento de Matemáticas, Facultad de Ciencias, Universidad de Cantabria, Santander, Spain
Email: gonzalem@ccaix3.unican.es

DOI: http://dx.doi.org/10.1090/S0002-9939-02-06386-4
PII: S 0002-9939(02)06386-4
Keywords: Quasi-nilpotent part, single valued extension property, operators with a generalized Kato decomposition
Received by editor(s): December 8, 2000
Received by editor(s) in revised form: April 20, 2001
Published electronically: March 12, 2002
Additional Notes: The research of the first two authors was supported by the International Cooperation Project between the University of Palermo (Italy) and Conicit-Venezuela
The research of the third author was supported by DGICYT, Spain
Communicated by: Joseph A. Ball
Article copyright: © Copyright 2002 American Mathematical Society