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2012

On Pythagoras' theorem for products of spectral triples

D'Andrea, Francesco, Martinetti, Pierre

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We discuss a version of Pythagoras theorem in noncommutative geometry.

Usual Pythagoras theorem can be formulated in terms of Connes' distance, between pure states, in the product of commutative spectral triples.
We investigate the generalization to both non pure states and arbitrary spectral triples.
We show that Pythagoras theorem is replaced by some Pythagoras inequalities, that we prove for the product of arbitrary (i.e.

On Pythagoras' theorem for products of spectral triples · Around

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2002

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2012

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