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WROCŁAW UNIVERSITY
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Contents of PMS, Vol. 43, Fasc. 2,
pages 241 - 246
DOI: 10.37190/0208-4147.00146
Published online 19.2.2024
 

An operator-valued free Poincarè inequality

Hyuga Ito

Abstract: The purpose of this short note is to give an operator-valued free Poincarè inequality, which provides a simple proof to (an improvement of) a lemma of Voiculescu (2000) asserting that the kernel of the free difference quotient is exactly the coefficients.

2010 AMS Mathematics Subject Classification: Primary 46L54; Secondary 46L52, 47B47.

Keywords and phrases: Sobolev space, free difference quotient, projective tensor product, conditional expectation, von Neumann algebra.

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