Holomorphically Weyl-decomposably regular. (English) Zbl 1391.35290
Summary: We consider left and right Fredholm-decomposably regular operators introduced in [S. Zhang et al., Banach J. Math. Anal. 7, No. 1, 41–58 (2013; Zbl 1288.47017)], and the corresponding holomorphic versions. Using their results established by Zhang et al. in [loc. cit.], we give new properties of these classes of operators. We introduce the concept of Weyl-decomposably regular operator and the corresponding holomorphic version in the setting of \(\mathcal L(X)\), where \(\mathcal L(X)\) is the set of all bounded operators from Banach space \(X\) to \(X\), and we give various characterizations of this class of operators.
MSC:
| 35P05 | General topics in linear spectral theory for PDEs |
| 47A05 | General (adjoints, conjugates, products, inverses, domains, ranges, etc.) |
| 35P20 | Asymptotic distributions of eigenvalues in context of PDEs |
| 35S05 | Pseudodifferential operators as generalizations of partial differential operators |
| 47A53 | (Semi-) Fredholm operators; index theories |
Keywords:
Fredholm and Kato non-singular operators; left (right) Fredholm-decomposably regular operators; left (right) holomorphically Fredholm-decomposably regular operators; Weyl operatorCitations:
Zbl 1288.47017References:
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