Idempotents of small norm
Jayden Mudge, Hung Le Pham

TL;DR
This paper characterizes idempotent functions of small norm in harmonic analysis, showing that such functions correspond to unions of cosets or open cosets in locally compact groups, depending on the group type.
Contribution
It proves new bounds on the norms of idempotents in Fourier and Fourier-Stieltjes algebras, resolving open questions for both abelian and non-abelian groups.
Findings
Idempotents with norm less than 4/3 in abelian groups are unions of two cosets.
Idempotents with cb-norm less than (1+√2)/2 in general groups are open cosets.
Provides a complete characterization of small-norm idempotents in harmonic analysis.
Abstract
Let be a locally compact group. We answer two questions left open in [7] and [9]: i) For abelian , we prove that if is an idempotent with norm , then is the union of two cosets of an open subgroup of . ii) For general , we prove that if is an idempotent with norm , then is an open coset in .
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Operator Algebra Research · Advanced Banach Space Theory · Advanced Topics in Algebra
