Remark

Tag 0CA7, permanent. Cite it as [Bourbaki, Tag 0CA7].

General Topology, chapter IX, Appendix 0. Infinite products in normed algebras

If $(x_n)$ is multipliable and its product is not a unit, the condition of Theorem 1 is not necessarily satisfied: for example, if all the $x_n$ are equal to the same element $x$ , where $\|x\| < 1$ , the sequence $(x_n)$ is multipliable and its product is 0, and for each non-empty finite subset $H$ of $\mathbf{N}$ , we have $\|p_H\| \leq \|x\| < 1 \leq \|e\|$ .

Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.

Cited by

Nothing.

Cites

Theorem 1