Journal of Lie Theory 31 (2021), No. 3, 599--624
Copyright Heldermann Verlag 2021
Commutators of Spectral Projections of Spin Operators
Ood Shabtai
School of Mathematical Sciences, Tel Aviv University, Tel Aviv, Israel
oodshabt@post.tau.ac.il
We present a proof that the operator norm of the commutator of certain spectral projections associated with spin operators converges to 1/2 in the semiclassical limit. The ranges of the projections are spanned by all eigenvectors corresponding to positive eigenvalues. The proof involves the theory of Hankel operators on the Hardy space. A discussion of several analogous results is also included, with an emphasis on the case of finite Heisenberg groups.
Keywords: Spectral projections, commutators, quantization.
MSC: 81S10; 53D50, 47B35, 17B.
[ Fulltext-pdf (995 KB)] for subscribers only.