Three-space theorem for semi-Fredholmness
Article
First Online:
Received:
- 153 Downloads
Abstract
A three-space theorem for upper semi-Fredholmness (resp. lower semi-Fredholmness) is proved.
Mathematics Subject Classification (2010)
47A53Keywords
Three-space theorem Semi-Fredholm operators Index Samuel multiplicityPreview
Unable to display preview. Download preview PDF.
References
- 1.Ambrozie C.-G., Vasilescu F.-H.: Banach space complexes. Kluwer Academic Publishers, Dordrecht-Boston-London (1995)MATHCrossRefGoogle Scholar
- 2.Barnes B.A.: Restrictions of bounded linear operators: closed range, Proc. Amer. Math. Soc. 135, 1735–1740 (2007)MATHCrossRefGoogle Scholar
- 3.Barnes B.A.: Spectral and Fredholm theory involving the diagonal of a bounded linear operator, Acta Sci. Math. (Szeged) 73, 237–250 (2007)MATHGoogle Scholar
- 4.Caradus S.R., Pfaffenberger W.E., Yood B.: Calkin algebras and algebras of operators on Banach spaces. Marcel Dekker, New York (1974)MATHGoogle Scholar
- 5.Castillo J.M.F., González M.: Three-space problems in Banach space theory. Springer-Verlag, Berlin-Heidelberg-New York (1997)MATHGoogle Scholar
- 6.Djordjević S.V., Duggal B.P.: Spectral properties of linear operator through invariant subspaces, Funct. Anal. Approx. Comput. 1, 19–29 (2009)Google Scholar
- 7.Djordjević S.V., Duggal B.P.: Drazin invertibility of the diagonal of an operator. Linear Multilinear Algebra 60, 65–71 (2012)MathSciNetMATHCrossRefGoogle Scholar
- 8.Fang X.: Samuel multiplicity and the structure of semi-Fredholm operators, Adv. Math. 186, 411–437 (2004)MATHGoogle Scholar
- 9.Grabiner S.: Uniform ascent and descent of bounded operators, J. Math. Soc. Japan 34, 317–337 (1982)MathSciNetMATHCrossRefGoogle Scholar
- 10.Grabiner S., Zemánek J.: Ascent, descent, and ergodic properties of linear operators, J. Operator Theory 48, 69–82 (2002)MathSciNetMATHGoogle Scholar
- 11.Harte R.: Invertibility and singularity for bounded linear operators. Marcel Dekker, New York (1988)MATHGoogle Scholar
- 12.Laursen, K.B., Neumann, M.M. An Introduction to Local Spectral Theory. Oxford University Press, 2000.Google Scholar
- 13.A. E. Taylor and D. C. Lay, Introduction to functional analysis, 2nd Edition, John Wiley and Sons, New York-Chichester-Brisbane-Toronto, 1980.Google Scholar
Copyright information
© Springer Basel 2012