Geodesic
r-FREDHOLM THEORY IN BANACH ALGEBRAS
Glasgow mathematical journal, Tome 61 (2019) no. 3, pp. 615-627

Voir la notice de l'article provenant de la source Cambridge University Press

Harte (1982, Math. Z.179, 431–436) initiated the study of Fredholm theory relative to a unital homomorphism T: A → B between unital Banach algebras A and B based on the following notions: an element a ∈ A is called Fredholm if 0 is not in the spectrum of Ta, while a is Weyl (Browder) if there exist (commuting) elements b and c in A with a = b + c such that 0 is not in the spectrum of b and c is in the null space of T. We introduce and investigate the concepts of r-Fredholm, r-Weyl and r-Browder elements, where 0 in these definitions is replaced by the spectral radii of a and b, respectively. 
BENJAMIN, RONALDA; LAUSTSEN, NIELS JAKOB; MOUTON, SONJA. r-FREDHOLM THEORY IN BANACH ALGEBRAS. Glasgow mathematical journal, Tome 61 (2019) no. 3, pp. 615-627. doi: 10.1017/S0017089518000393
@article{10_1017_S0017089518000393,
     author = {BENJAMIN, RONALDA and LAUSTSEN, NIELS JAKOB and MOUTON, SONJA},
     title = {r-FREDHOLM {THEORY} {IN} {BANACH} {ALGEBRAS}},
     journal = {Glasgow mathematical journal},
     pages = {615--627},
     year = {2019},
     volume = {61},
     number = {3},
     doi = {10.1017/S0017089518000393},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089518000393/}
}
TY  - JOUR
AU  - BENJAMIN, RONALDA
AU  - LAUSTSEN, NIELS JAKOB
AU  - MOUTON, SONJA
TI  - r-FREDHOLM THEORY IN BANACH ALGEBRAS
JO  - Glasgow mathematical journal
PY  - 2019
SP  - 615
EP  - 627
VL  - 61
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.1017/S0017089518000393/
DO  - 10.1017/S0017089518000393
ID  - 10_1017_S0017089518000393
ER  - 
%0 Journal Article
%A BENJAMIN, RONALDA
%A LAUSTSEN, NIELS JAKOB
%A MOUTON, SONJA
%T r-FREDHOLM THEORY IN BANACH ALGEBRAS
%J Glasgow mathematical journal
%D 2019
%P 615-627
%V 61
%N 3
%U http://geodesic.mathdoc.fr/articles/10.1017/S0017089518000393/
%R 10.1017/S0017089518000393
%F 10_1017_S0017089518000393

[1] Alekhno, E. A., Some properties of essential spectra of a positive operator, Positivity 11 (2007), 375–386. Google Scholar | DOI

[2] Alekhno, E. A., Some properties of essential spectra of a positive operator, II, Positivity 13 (2009), 3–20. Google Scholar | DOI

[3] Aupetit, B., A primer on spectral theory (Springer-Verlag, New York, 1991). Google Scholar | DOI

[4] Benjamin, R. and Mouton, S., Fredholm theory in ordered Banach algebras, Quaest. Math. 39 (2016), 643–664. Google Scholar | DOI

[5] Benjamin, R. and Mouton, S., The upper Browder spectrum property, Positivity 21 (2017), 575–592. Google Scholar | DOI

[6] Caradus, S. R., Pfaffenberger, W. E. and Yood, B., Calkin algebras and algebras of operators on Banach spaces (Marcel Dekker, Inc., New York, 1974). Google Scholar

[7] Conway, J. B., Functions of one complex variable I, 2nd edition (Springer, New York, 1978). Google Scholar | DOI

[8] Grobler, J. J. and Raubenheimer, H., Spectral properties of elements in different Banach algebras, Glasgow Math. J. 33 (1991), 11–20. Google Scholar | DOI

[9] Harte, R. E., The exponential spectrum in Banach algebras, Proc. Amer. Math. Soc. 58 (1976), 114–118. Google Scholar | DOI

[10] Harte, R. E., Fredholm theory relative to a Banach algebra homomorphism, Math. Z. 179 (1982), 431–436. Google Scholar | DOI

[11] Harte, R. E., Fredholm, Weyl and Browder theory, Proc. Roy. Irish Acad. Sect. A 85 (1985), 151–176. Google Scholar

[12] Harte, R. E., Fredholm, Weyl and Browder theory II, Proc. Roy. Irish Acad. Sect. A 91 (1991), 79–88. Google Scholar

[13] Koliha, J. J., A generalized Drazin inverse, Glasgow Math. J. 38 (1996), 367–381. Google Scholar | DOI

[14] Lebow, A. and Schechter, M., Semigroups of operators and measures of noncompactness, J. Funct. Anal. 7 (1971), 1–26. Google Scholar | DOI

[15] Lindeboom, L. and Raubenheimer, H., On regularities and Fredholm theory, Czechoslovak Math. J. 52 (2002), 565–574. Google Scholar | DOI

[16] Mathieu, M. and Schick, G. J., First results on spectrally bounded operators, Studia Math. 152 (2002), 187–199. Google Scholar | DOI

[17] Du, H. Mouton, T., Mouton, S. and Raubenheimer, H., Ruston elements and Fredholm theory relative to arbitrary homomorphisms, Quaest. Math. 34 (2011), 341–359. Google Scholar

[18] Du, H. Mouton, T. and Raubenheimer, H., Fredholm theory relative to two Banach algebra homomorphisms, Quaest. Math. 14 (1991), 371–382. Google Scholar

[19] Du, H. Mouton, T. and Raubenheimer, H., More on Fredholm theory relative to a Banach algebra homomorphism, Proc. Roy. Irish Acad. Sect. A 93 (1993), 17–25. Google Scholar

[20] Mouton, S., A spectral problem in ordered Banach algebras, Bull. Austral. Math. Soc. 67 (2003), 131–144. Google Scholar | DOI

[21] Willard, S., General topology (Addison-Wesley, Reading, Massachusetts, 1970). Google Scholar

Cité par Sources :