# A note on topologically nilpotent Banach algebras

Studia Mathematica (1992)

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

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topDixon, 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

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

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