An operator-valued free Poincarè inequality
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.