Nonstandard Ideals in Radical Convolution Algebras on a Half-Line
Canadian journal of mathematics, Tome 39 (1987) no. 2, pp. 309-321

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

This note is about the interplay between two classes of radical Banach algebras, and we begin by describing the algebras in question.A weight sequence is a positive sequence w = (wn ) defined on Z + (the non-negative integers) and satisfying w 0 = 1 and wm+n ≦ wmwn for all m and n in Z +. For such a sequence w, the Banach space is a Banach algebra with respect to the convolution product, defined by
Dales, H. G.; McClure, J. P. Nonstandard Ideals in Radical Convolution Algebras on a Half-Line. Canadian journal of mathematics, Tome 39 (1987) no. 2, pp. 309-321. doi: 10.4153/CJM-1987-014-8
@article{10_4153_CJM_1987_014_8,
     author = {Dales, H. G. and McClure, J. P.},
     title = {Nonstandard {Ideals} in {Radical} {Convolution} {Algebras} on a {Half-Line}},
     journal = {Canadian journal of mathematics},
     pages = {309--321},
     year = {1987},
     volume = {39},
     number = {2},
     doi = {10.4153/CJM-1987-014-8},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1987-014-8/}
}
TY  - JOUR
AU  - Dales, H. G.
AU  - McClure, J. P.
TI  - Nonstandard Ideals in Radical Convolution Algebras on a Half-Line
JO  - Canadian journal of mathematics
PY  - 1987
SP  - 309
EP  - 321
VL  - 39
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1987-014-8/
DO  - 10.4153/CJM-1987-014-8
ID  - 10_4153_CJM_1987_014_8
ER  - 
%0 Journal Article
%A Dales, H. G.
%A McClure, J. P.
%T Nonstandard Ideals in Radical Convolution Algebras on a Half-Line
%J Canadian journal of mathematics
%D 1987
%P 309-321
%V 39
%N 2
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1987-014-8/
%R 10.4153/CJM-1987-014-8
%F 10_4153_CJM_1987_014_8

[1] 1. Allan, G. R., Ideals of rapidly growing functions, Proceedings International Symposium on Functional Analysis and its Applications, Ibadan, Nigeria (1977). Google Scholar

[2] 2. Bachar, J. M. et al., Editors, Radical Banach algebras and automatic continuity. Lecture notes in Mathematics 975 (Springer-Verlag, Berlin and New York, 1983). Google Scholar | DOI

[3] 3. Bade, W. G. and Dales, H. G., Norms and ideals in radical convolution algebras, J. Functional Analysis 41 (1981), 77–109. Google Scholar

[4] 4. Bade, W. G., Dales, H. G. and Laursen, K. B., Multipliers of radical Banach algebras of power series, Mem. American Math. Soc. 303 (Providence, R.I., 1984). Google Scholar

[5] 5. Domar, Y., Cyclic elements under translation in weighted L1 spaces on + , Ark. Mat. 19 (1981), 137–144. Google Scholar

[6] 6. Domar, Y., A solution of the translation-invariant subspace problem for weighted Lp on , +, or , in [2], 214–226. Google Scholar

[7] 7. Gelfand, I., Raikov, D. and Sĭlov, , Commutative normed rings (Chelsea, New York, 1964). Google Scholar

[8] 8. Grabiner, S., A formal power series operational calculus for quasinilpotent operators II, J. Math. Anal. Appl. 43 (1973), 170–192. Google Scholar

[9] 9. Grabiner, S., Weighted shifts and Banach algebras of power series, American J. Math. 97 (1975), 16–42. Google Scholar

[10] 10. Grabiner, S. and Thomas, M. P., Non-unicellular strictly cyclic quasinilpotent shifts on Banach spaces, J. Operator Theory 13 (1985), 163–170. Google Scholar

[11] 11. Hille, E. and Phillips, R. S., Functional analysis and semi-groups, American Math. Soc. Colloquium Publications 31 (Providence, R. F, 1957). Google Scholar

[12] 12. Nikolskiĭ, N. K., Selected problems of weighted approximation and spectral analysis, Proc. Steklov Inst. Math. 720 (1974) (American Math. Soc. Translation, 1976). Google Scholar

[13] 13. Shields, A. L., Weighted shift operators and analytic function theory, in Topics in operator theory, American Math. Soc. Mathematical Surveys 13 (Providence, R. I., 1974). Google Scholar

[14] 14. Thomas, M. P., Closed ideals and biorthogonal systems in radical Banach algebras of power series, Proc. Edinburgh Math. Soc. 25 (1982), 245–257. Google Scholar

[15] 15. Thomas, M. P., Closed ideals of l1{ω} when {ω} is star-shaped, Pacific J. Math. 105 (1983), 237–255. Google Scholar

[16] 16. Thomas, M. P., Approximation in the radical algebra l1{ω} when {ω} is star-shaped, in [2], 258–272. Google Scholar

[17] 17. Thomas, M. P., A nonstandard ideal of a radical Banach algebra of power series, Acta Math. 152 (1984), 199–217. Google Scholar

[18] 18. Thomas, M. P., Quasinilpotent strictly cyclic unilateral weighted shift operators on lp which are not unicellular, Proc. London Math. Soc. (3) 51 (1985), 127–145. Google Scholar

Cité par Sources :