- Tytuł:
- Series representation of compact linear operators in Banach spaces
- Autorzy:
-
Edmunds, David E.
Lang, Jan - Powiązania:
- https://bibliotekanauki.pl/articles/745232.pdf
- Data publikacji:
- 2016
- Wydawca:
- Polskie Towarzystwo Matematyczne
- Tematy:
-
Eigenvalues
Banach spaces
compact operators
nuclear maps
Gelfand numbers - Opis:
- Let \(p\in(1,\infty)\) and \(I=(0,1)\); suppose that \(T\colon L_{p}(I)\rightarrow L_{p}(I)\) is a~compact linear map with trivial kernel and range dense in \(L_{p}(I)\). It is shown that if the Gelfand numbers of \(T\) decay sufficiently quickly, then the action of \(T\) is given by a series with calculable coefficients. The special properties of \(L_{p}(I)\) enable this to be established under weaker conditions on the Gelfand numbers than in earlier work set in the context of more general spaces.
- Źródło:
-
Commentationes Mathematicae; 2016, 56, 1
0373-8299 - Pojawia się w:
- Commentationes Mathematicae
- Dostawca treści:
- Biblioteka Nauki
Artykuł