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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

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.

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