Journal of Lie Theory

no. 3
Commutators of Spectral Projections of Spin Operators
Journal of Lie Theory, Volume 31 (2021) no. 3, pp. 599-624
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.
DOI: 10.5802/jolt.1188
Classification: 81S10, 53D50, 47B35, 17B
Keywords: Spectral projections, commutators, quantization 
@article{JOLT_2021_31_3_a0,
     author = {O. Shabtai},
     title = {Commutators of {Spectral} {Projections} of {Spin} {Operators}},
     journal = {Journal of Lie Theory},
     pages = {599--624},
     year = {2021},
     volume = {31},
     number = {3},
     doi = {10.5802/jolt.1188},
     zbl = {1468.81059},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.1188/}
}
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O. Shabtai. Commutators of Spectral Projections of Spin Operators. Journal of Lie Theory, Volume 31 (2021) no. 3, pp. 599-624. doi: 10.5802/jolt.1188

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