Comment on `The tan θ theorem with relaxed conditions', by Y. Nakatsukasa

Details Comment on `The tan θ theorem with relaxed conditions', by Y. Nakatsukasa Comment on `The tan θ theorem with relaxed conditions', by Y. Nakatsukasa

2012-04-19

arxiv.org/abs/1204.4441v1

Mathematics

Spectral Theory

Scientific paper

We show that in case of the spectral norm, one of the main results of the recent paper `The tan {\theta} theorem with relaxed conditions', by Yuji Nakatsukasa, published in Linear Algebra and its Applications is a corollary of the tan {\theta} theorem proven in [V.Kostrykin, K.A.Makarov, and A.K.Motovilov, On the existence of solutions to the operator Riccati equation and the tan {\theta} theorem, IEOT 51 (2005), 121-140; doi:10.1007/s00020-003-1248-6]. We also give an alternative finite-dimensional matrix formulation of another tan {\theta} theorem proven in [S.Albeverio and A.K.Motovilov, The a priori tan {\theta} theorem for spectral subspaces, arXiv:1012.1569].

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