Pith. sign in

REVIEW

$B$-valued semi-circular system and the free Poincar\'{e} inequality

Not yet reviewed by Pith; the record is open.

Re-run · record.json Download PDF Read on arXiv ↗

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 2409.16498 v3 pith:S6JH2VIL submitted 2024-09-24 math.OA math.RA

Hyuga Ito This is my paper · ORCID
classification math.OAmath.RA
keywords valuedfreeinequalitypoincarcitesemi-circularsystemtheorem
verification ladder T0 review T1 audit T2 compute T3 formal

Signed reviews

No signed human review yet.

0 comments
abstract

We characterize $B$-valued semi-circular system in terms of $B$-valued free probabilistic analogue of Poincar\'{e} inequality. This is a $B$-valued generalization of Biane's theorem \cite[Theorem 5.1]{b03}. Moreover, we prove that Voiculescu's conjecture on $B$-valued free Poincar\'{e} inequality in \cite{aim06} is not in the affirmative as it is.

Discussion (0). Continue with ORCID to comment.

Pith tools