# Difference between revisions of "Talk:Automatic continuity for Banach algebras"

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The sentence "What algebraic conditions on $A$ and/or $B$ ensure that the homomorphism $\theta$ is automatically continuous?" is a little confusing to the non-expert. It suggests that there is some special form of continuity called "automatic continuity", in the same way that one speaks of "uniformly continuous", for example. It would help the general reader to write, for example "$\ldots\ \theta$ is <u>necessarily</u> continuous", as Garth Dales does in the introduction to his 1978 survey paper. [[User:Richard Pinch|Richard Pinch]] ([[User talk:Richard Pinch|talk]]) 20:19, 8 March 2018 (CET) | The sentence "What algebraic conditions on $A$ and/or $B$ ensure that the homomorphism $\theta$ is automatically continuous?" is a little confusing to the non-expert. It suggests that there is some special form of continuity called "automatic continuity", in the same way that one speaks of "uniformly continuous", for example. It would help the general reader to write, for example "$\ldots\ \theta$ is <u>necessarily</u> continuous", as Garth Dales does in the introduction to his 1978 survey paper. [[User:Richard Pinch|Richard Pinch]] ([[User talk:Richard Pinch|talk]]) 20:19, 8 March 2018 (CET) | ||

+ | :I agree. [[User:Boris Tsirelson|Boris Tsirelson]] ([[User talk:Boris Tsirelson|talk]]) 22:05, 8 March 2018 (CET) |

## Latest revision as of 22:05, 8 March 2018

## Terminology

The sentence "What algebraic conditions on $A$ and/or $B$ ensure that the homomorphism $\theta$ is automatically continuous?" is a little confusing to the non-expert. It suggests that there is some special form of continuity called "automatic continuity", in the same way that one speaks of "uniformly continuous", for example. It would help the general reader to write, for example "$\ldots\ \theta$ is __necessarily__ continuous", as Garth Dales does in the introduction to his 1978 survey paper. Richard Pinch (talk) 20:19, 8 March 2018 (CET)

- I agree. Boris Tsirelson (talk) 22:05, 8 March 2018 (CET)

**How to Cite This Entry:**

Automatic continuity for Banach algebras.

*Encyclopedia of Mathematics.*URL: http://www.encyclopediaofmath.org/index.php?title=Automatic_continuity_for_Banach_algebras&oldid=42931