|
On Drazin invertibility
Author(s):
Pietro
Aiena;
Maria
T.
Biondi;
Carlos
Carpintero
Journal:
Proc. Amer. Math. Soc.
136
(2008),
2839-2848.
MSC (2000):
Primary 47A10, 47A11;
Secondary 47A53, 47A55
Posted:
March 28, 2008
Retrieve article in:
PDF DVI PostScript
Abstract |
References |
Similar articles |
Additional information
Abstract:
The left Drazin spectrum and the Drazin spectrum coincide with the upper semi- -Browder spectrum and the  -Browder spectrum, respectively. We also prove that some spectra coincide whenever  or  satisfies the single-valued extension property.
References:
-
- 1.
- P. Aiena. Fredholm and local spectral theory, with applications to multipliers. Kluwer Acad. Publishers (2004). MR 2070395 (2005e:47001)
- 2.
- P. Aiena. Quasi-Fredholm operators and localized SVEP. Acta Sci. Math. (Szeged) 73, (2007), nos. 1-2, 251-263. MR 2339864
- 3.
- P. Aiena, M. T. Biondi. Browder's theorems through localized SVEP. Mediterranean Jour. of Math. 2, (2005), 137-151. MR 2184191 (2006h:47003)
- 4.
- P. Aiena, C. Carpintero, E. Rosas. Some characterizations of operators satisfying
 -Browder's theorem. J. Math. Anal. Appl. 311, (2005), 530-544. MR 2168416 (2006e:47005) - 5.
- P. Aiena, M. L. Colasante, M. González. Operators which have a closed quasi-nilpotent part, Proc. Amer. Math. Soc. 130, (9) (2002), 2701-2710. MR 1900878 (2003g:47008)
- 6.
- P. Aiena, T. L. Miller. On generalized
 -Browder's theorem. Studia Math. 180, (2007), no. 3, 285-300. MR 2314082 - 7.
- P. Aiena, O. Garcia. Generalized Browder's theorem and SVEP. Mediterranean Jour. of Math. 4, (2007), no. 2, 215-228. MR 2340481
- 8.
- M. Amouch, H. Zguitti. On the equivalence of Browder's and generalized Browder's theorem. Glasgow Math. Jour. 48, (2006), 179-185. MR 2224938 (2007a:47002)
- 9.
- M. Berkani. On a class of quasi-Fredholm operators. Int. Equa. Oper. Theory 34 (1), (1999), 244-249. MR 1694711 (2000d:47023)
- 10.
- M. Berkani. Restriction of an operator to the range of its powers, Studia Math. 140 (2), (2000), 163-175. MR 1784630 (2001g:47021)
- 11.
- M. Berkani. Index of B-Fredholm operators and generalization of a Weyl theorem, Proc. Amer. Math. Soc. 130, (2002), no. 6, 1717-1723. MR 1887019 (2002k:47028)
- 12.
- M. Berkani, J. J. Koliha. Weyl type theorems for bounded linear operators, Acta Sci. Math. (Szeged) 69, (2003), nos. 1-2, 359-376. MR 1991673 (2004c:47005)
- 13.
- M. Berkani, M. Sarih. On semi B-Fredholm operators, Glasgow Math. J. 43, (2001), 457-465. MR 1878588 (2002j:47017)
- 14.
- M. P. Drazin. Pseudo-inverses in associative rings and semigroups. Amer. Math. Monthly 65, (1958), 506-514. MR 0098762 (20:5217)
- 15.
- B. P. Duggal. SVEP and generalized Weyl's theorem. (2006), Mediterranean Jour. of Math. 4, (2007), no. 3, 309-320. MR 2349890
- 16.
- S. Grabiner. Uniform ascent and descent of bounded operators, J. Math. Soc. Japan 34, (1982), 317-337. MR 651274 (84a:47003)
- 17.
- H. Heuser. Functional Analysis, John Wiley & Sons, Chichester, 1982. MR 0640429 (83m:46001)
- 18.
- J. J. Koliha. Isolated spectral points, Proc. Amer. Math. Soc. 124, (1996), 3417-3424. MR 1342031 (97a:46057)
- 19.
- D. C. Lay. Spectral analysis using ascent, descent, nullity and defect, Math. Ann. 184, (1969/1970), 197-214. MR 0259644 (41:4279)
- 20.
- K. B. Laursen, M. M. Neumann. An introduction to local spectral theory, The Clarendon Press, Oxford University Press, New York, 2000. MR 1747914 (2001k:47002)
- 21.
- M. Mbekhta, V. Müller. On the axiomatic theory of the spectrum. II. Studia Math. 119, (1996), 129-147. MR 1391472 (97c:47005)
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 Metodi e Modelli Matematici, Facoltà di Ingegneria, Università di Palermo, Viale delle Scienze, I-90128 Palermo, Italy
Email:
paiena@unipa.it
Maria
T.
Biondi
Affiliation:
Departamento de Matemáticas, Facultad de Ciencias, Universidad UCLA de Barquisimeto, Venezuela
Email:
mtbiondi@hotmail.com
Carlos
Carpintero
Affiliation:
Departamento de Matemáticas, Facultad de Ciencias, Universidad de Oriente, Cumaná, Venezuela
Email:
ccarpi@sucre.edu.udo.ve
DOI:
10.1090/S0002-9939-08-09138-7
PII:
S 0002-9939(08)09138-7
Keywords:
Localized SVEP,
$B$-Browder operators,
Drazin invertibility
Received by editor(s):
November 3, 2006,
Received by editor(s) in revised form:
February 26, 2007
Posted:
March 28, 2008
Communicated by:
Joseph A. Ball
Copyright of article:
Copyright
2008,
American Mathematical Society
|
Comments: webmaster@ams.org