Notes on the sin 2 circle minus Theorem

作者：Seelmann Albrecht^*

来源：Integral Equations and Operator Theory, 2014, 79(4): 579-597.

DOI：10.1007/s00020-014-2127-z

• Subspace perturbation problem
• operator angle
• maximal angle between closed subspaces
• Sylvester equation
• Riccati equation
• symmetrically-normed ideal

An analogue of the Davis-Kahan theorem from (SIAM J Numer Anal 7:1-46, 1970) is proved under a general spectral separation condition. This extends the generic estimates recently shown by Albeverio and Motovilov in (Complex Anal Oper Theory 7:1389-1416, 2013). The result is applied to the subspace perturbation problem to obtain a bound on the arcsine of the norm of the difference of the spectral projections associated with isolated components of the spectrum of the unperturbed and perturbed operators, respectively.

• 出版日期2014-8