Research partly supported by NSF Grant No. MCS-8002923.
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References
G. R. Allan, Ideals of rapidly growing functions, Proceedings International Symposium on Functional Analysis and its Applications, Ibadan, Nigeria (1977).
W. G. Bade and H. G. Dales, Norms and ideals in radical convolution algebras, J. Functional Analysis, 41 (1981), 77–109.
Y. Domar, Extensions of the Titchmarsh convolution theorem with applications in the theory of invariant subspaces, Proc. London Math. Soc., to appear.
_____, A solution of the translation-invariant subspace problem for weighted L1 on ℝ and ℝ+, this Volume.
F. Ghahramani, Homomorphisms and derivations on weighted convolution algebras, J. London Math. Soc., 21 (1980), 149–161.
S. Grabiner, A formal power series operational calculus for quasinilpotent operators, Duke Math. J., 38 (1971), 641–658.
_____, A formal power series operational calculus for quasinilpotent operators, II, J. Math. Anal. Appl., 43 (1973), 170–192.
_____, Derivations and automorphisms of Banach algebras of power series, Mem. Amer. Math. Soc., 146 (1974).
_____, Weighted shifts and Banach algebras of power series, Amer. J. Math., 97 (1975), 16–42.
_____, Weighted convolution algebras on the half line, J. Math. Anal. Appl., 83 (1981), 531–553.
E. Hewitt and K. A. Ross, Abstract Harmonic Analysis, I, Springer-Verlag, Berlin, 1963.
E. Hille and R. S. Phillips, Functional Analysis and Semi-groups, American Mathematical Society, Providence, R.I., 1957.
H. Kamowitz and S. Scheinberg, Derivations and automorphisms of L1(0,1), Trans. Amer. Math. Soc., 135(1969), 415–427.
N. K. Nikolskii, Selected problems of weighted approximation and spectral analysis, Proc. Steklov Inst. Math., 120 (1974).
A. W. Roberts and D. E. Varberg, Convex Functions, Academic Press, New York, 1973.
W. Rudin, Functional Analysis, McGraw-Hill, New York, 1973.
M. P. Thomas, Closed ideals of l1(ωn) when {ωn} is star-shaped, Pacific J. Math., to appear.
_____, Approximation in the radical algebra l1(ωn) when {ωn} is star-shaped, this Volume.
A. Zygmund, Trigonometric Series, Volume 1, Cambridge University Press, Cambridge, England, 1959.
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Grabiner, S. (1983). Weighted convolution algebras as analogues of Banach algebras of power series. In: Bachar, J.M., Bade, W.G., Curtis, P.C., Dales, H.G., Thomas, M.P. (eds) Radical Banach Algebras and Automatic Continuity. Lecture Notes in Mathematics, vol 975. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0064559
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DOI: https://doi.org/10.1007/BFb0064559
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