NONCOMMUTATIVE COTLAR IDENTITIES FOR GROUPS ACTING ON TREE-LIKE STRUCTURES
Abstract
Abstract Let T m $T_m$ upper T Subscript m be a noncommutative Fourier multiplier. In recent work, Mei and Ricard introduced a noncommutative analogue of Cotlar's identity to prove that certain multipliers are bounded on the noncommutative L p $L_p$ upper L Subscript p -spaces of a free group. Here, we study Cotlar-type identities in full generality, giving a closed characterization for them in terms of m : ( m ( g h ) − m ( g ) ) ( m ( g − 1 ) − m ( h ) ) = 0 , ∀ g ∈ G ∖ { e } , h ∈ G . $$\begin{align*}\big( m(g h) - m(g) \big) \, \big( m(g^{-1}) - m(h) \big) = 0, \; \forall g \in \mathrm{G}\setminus \{e\}, h \in \mathrm{G}. \end{align*}$$ Using a geometric argument, we prove that if X is a tree —or more generally an R $\mathbb{R}$ double struck upper R -tree— on which G $\mathrm{G}$ normal upper G
Fields of Study & Subjects
Advanced Operator Algebra Research
Advanced Algebra and Geometry
Geometric and Algebraic Topology
Publication details
- Journal / source
- Journal of the Institute of Mathematics of Jussieu
- Publisher
- Cambridge University Press (CUP)
- Volume
- 25
- Issue
- 5
- Pages
- 2623–2670
- Publication date
- 20 July 2026
- Language
- EN