Bourbaki

Remark

Tag 02EO, permanent. Cite it as [Bourbaki, Tag 02EO].

Théories spectrales, chapter I, § 6. Algèbres stellaires

In general, if xx and yy are positive elements of a *-algebra A, the condition 0⩽x⩽y0\leqslant x\leqslant y does not imply x2⩽y2(x^2\leqslant y^2(cf. exercise 15 of I, p. 182).

Bourbaki sets the proof directly after the statement, and the corpus does not separate them, so what is above is the statement and its proof together.

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Cites

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Machine translation of the English, by gpt-5-6-mini, gpt-5.4, against glossary version 34. Not checked by a person. That model is a cut down version of the one the rest of this language was written by.