Wei, Feng and Zhang, Yuhao (2022) LIE-TYPE DERIVATIONS OF NEST ALGEBRAS ON BANACH SPACES AND RELATED TOPICS. JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 112 (3). pp. 391-430. ISSN 1446-7887, 1446-8107
Full text not available from this repository. (Request a copy)Abstract
Let X be a Banach space over the complex field C and B(X) be the algebra of all bounded linear operators on X. Let N be a nontrivial nest on X, AlgN be the nest algebra associated with N, and L: AlgN -> B(X) be a linear mapping. Suppose that p(n)(x(1), x(2), ..., x(n)) is an (n - 1)th commutator defined by n indeterminates x(1), x(2), ..., x(n). It is shown that L satisfies the rule L(p(n)(A(1), A(2), ..., A(n))) = Sigma(n)(k=1) p(n)(A(1), ..., A(k-1), L(A(k)), A(k+1), ...,A(n)) for all A(1), A(2), ..., A(n) AlgN if and only if there exist a linear derivation D: AlgN -> B(X) and a linear mapping H: AlgN -> CI vanishing on each (n - 1)th commutator p(n) (A(1), A(2), ..., A(n)) for all A(1), A(2), ...,A(n) is an element of AlgN such that L(A) = D (A) + H (A) for all A is an element of AlgN. We also propose some related topics for future research.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | TRIPLE DERIVATIONS; N-DERIVATIONS; BIDERIVATIONS; ISOMORPHISMS; MAPS; Lie-type derivation; nest algebra; rank-one operator |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics |
| Depositing User: | Petra Gürster |
| Date Deposited: | 08 Feb 2023 11:09 |
| Last Modified: | 08 Feb 2023 11:09 |
| URI: | https://pred.uni-regensburg.de/id/eprint/46963 |
Actions (login required)
 |
View Item |
