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Two-sided bounds and perturbation results for regularized determinants of infinite order compact operators. (English) Zbl 1151.47003

A compact operator in a separable Hilbert space is called of infinite order if it does not belong to any Schatten-von Neumann ideal [cf. M. G. Kreĭn and I. C. Gohberg, “Theory and applications of Volterra operators in Hilbert space” (Translations of Mathematical Monographs 24, AMS, Providence/RI) (1970; Zbl 0194.43804)]. In the present paper, the author extends some results on determinants of Schatten-von Neumann operators to infinite order operators by presenting some upper and lower bounds for the regularized determinants of infinite order operators and gives some perturbation results.

MSC:

47A05 General (adjoints, conjugates, products, inverses, domains, ranges, etc.)
47A55 Perturbation theory of linear operators

Citations:

Zbl 0194.43804
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References:

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