Series representation of compact linear operators in Banach spaces

• Autorzy: David E. Edmunds , Jan Lang
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Eigenvalues; Banach spaces; compact operators; nuclear maps; Gelfand numbers

• Wydawca: Polish Mathematical Society
• Czasopismo: Commentationes Mathematicae
• Rocznik: 2016
• Tom: 56
• Numer: 1

Daty

wydano

2016

online

2016-05-27

Twórcy

autor

David E. Edmunds

autor

Jan Lang

Identyfikatory

DOI

10.14708/cm.v56i1.1139