Abstract
A general theory of regularized and Hilbert-Carleman determinants in norrned algebras of operators acting in Banach spaces is proposed. In this approach regularized determinants are defined as continuous extensions of the corresponding determinants of finite dimensional operators. We characterize the algebras for which such extensions exist, describe the mam properties of the extended determinants obtain Cramer's rule and the formulas for the resolvent which are expressed via the extended traces tr(Ak) of iterations and regularized determinants. This paper is a continuation of the paper [GGKr].
| Original language | English |
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| Pages (from-to) | 10-47 |
| Number of pages | 38 |
| Journal | Integral Equations and Operator Theory |
| Volume | 27 |
| Issue number | 1 |
| DOIs | |
| State | Published - 1997 |