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Semigroup domination and eigenvalue estimates. (English. Russian original) Zbl 1015.47023
St. Petersbg. Math. J. 12, No. 5, 831-845 (2001); translation from Algebra Anal. 12, No. 5, 158-177 (2001).
Using the domination $$|e^{-tS}|\leq e^{-tT}$$, $$t \geq 0$$, between two selfadjoint semigroups $$(e^{-tS})_{t\geq 0}$$ and $$(e^{-tT})_{t\geq 0 }$$ on $$L^2$$-spaces, the author obtains eigenvalue estimates for $$S$$ from the ones for $$T$$. Applications to magnetic Schrödinger operators are given.

##### MSC:
 47D06 One-parameter semigroups and linear evolution equations 35P15 Estimates of eigenvalues in context of PDEs 47A10 Spectrum, resolvent 47B38 Linear operators on function spaces (general) 47B65 Positive linear operators and order-bounded operators