The TAN $2\Theta$ Theorem for Indefinite Quadratic Forms
Luka Grubi\v{s}i\'c, Vadim Kostrykin, Konstantin A. Makarov,, Kre\v{s}imir Veseli\'c
TL;DR
This paper extends the Davis-Kahan Tan 2Theta theorem to indefinite quadratic forms, broadening its applicability to a wider class of linear operators beyond semibounded cases.
Contribution
It generalizes the Tan 2Theta theorem to indefinite quadratic forms, providing a new theoretical result for a broader class of operators.
Findings
Proves a version of the Tan 2Theta theorem for indefinite quadratic forms.
Generalizes recent results by Motovilov and Selin.
Enhances understanding of spectral perturbation for non-semibounded operators.
Abstract
A version of the Davis-Kahan Tan theorem [SIAM J. Numer. Anal. \textbf{7} (1970), 1 -- 46] for not necessarily semibounded linear operators defined by quadratic forms is proven. This theorem generalizes a recent result by Motovilov and Selin [Integr. Equat. Oper. Theory \textbf{56} (2006), 511 -- 542].
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