A note on topologically nilpotent Banach algebras

• Autorzy: P. G. Dixon , V. Müller
• Języki publikacji: EN

Abstrakty

EN

A Banach algebra A is said to be topologically nilpotent if $sup{∥x₁... ...x_n∥^{1/n}: x_i ∈ A, ∥x_i∥ ≤ 1 (1 ≤ i ≤ n)}$ tends to 0 as n → ∞. We continue the study of topologically nilpotent algebras which was started in [2]

Kategorie tematyczne

• 46H05: General theory of topological algebras

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1992
• Tom: 102
• Numer: 3
• Strony: 269-275

Daty

wydano

1992

otrzymano

1991-12-12

Twórcy

autor

P. G. Dixon

• Department of Pure Mathematics, University of Sheffield, Sheffield, S3 7RH, England

autor

V. Müller

• Institute of Mathematics, Czechoslovak Academy of Sciences, Žitná 25, 115 67 Praha 1, Czechoslovakia

Bibliografia

• [1] F. F. Bonsall and J. Duncan, Complete Normed Algebras, Springer, Berlin 1973.
• [2] P. G. Dixon, Topologically nilpotent Banach algebras and factorization, Proc. Roy. Soc. Edinburgh Sect. A 119 (1991), 329-341.
• [3] P. G. Dixon and G. A. Willis, Approximate identities in extensions of topologically nilpotent Banach algebras, Proc. Roy. Soc. Edinburgh Sect. A, to appear.
• [4] S. Grabiner, The nilpotency of Banach nil algebras, Proc. Amer. Math. Soc. 21 (1969), 510.
• [5] G. Higman, On a conjecture of Nagata, Proc. Cambridge Philos. Soc. 52 (1956), 1-4.