A note on topologically nilpotent Banach algebras

P. Dixon; V. Müller

Studia Mathematica (1992)

  • Volume: 102, Issue: 3, page 269-275
  • ISSN: 0039-3223

Abstract

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A Banach algebra A is said to be topologically nilpotent if s u p ∥ x ₁ . . . . . . 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]

How to cite

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Dixon, P., and Müller, V.. "A note on topologically nilpotent Banach algebras." Studia Mathematica 102.3 (1992): 269-275. <http://eudml.org/doc/215928>.

@article{Dixon1992,
abstract = {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]},
author = {Dixon, P., Müller, V.},
journal = {Studia Mathematica},
keywords = {topologically nilpotent Banach algebras},
language = {eng},
number = {3},
pages = {269-275},
title = {A note on topologically nilpotent Banach algebras},
url = {http://eudml.org/doc/215928},
volume = {102},
year = {1992},
}

TY - JOUR
AU - Dixon, P.
AU - Müller, V.
TI - A note on topologically nilpotent Banach algebras
JO - Studia Mathematica
PY - 1992
VL - 102
IS - 3
SP - 269
EP - 275
AB - 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]
LA - eng
KW - topologically nilpotent Banach algebras
UR - http://eudml.org/doc/215928
ER -

References

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  1. [1] F. F. Bonsall and J. Duncan, Complete Normed Algebras, Springer, Berlin 1973. Zbl0271.46039
  2. [2] P. G. Dixon, Topologically nilpotent Banach algebras and factorization, Proc. Roy. Soc. Edinburgh Sect. A 119 (1991), 329-341. Zbl0762.46039
  3. [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. Zbl0799.46060
  4. [4] S. Grabiner, The nilpotency of Banach nil algebras, Proc. Amer. Math. Soc. 21 (1969), 510. Zbl0174.44602
  5. [5] G. Higman, On a conjecture of Nagata, Proc. Cambridge Philos. Soc. 52 (1956), 1-4. Zbl0072.02502

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