Explicit representation of compact linear operators in Banach spaces via polar sets

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

Abstrakty

EN

We consider a compact linear map T acting between Banach spaces both of which are uniformly convex and uniformly smooth; it is supposed that T has trivial kernel and range dense in the target space. 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. This provides a Banach space version of the well-known Hilbert space result of E. Schmidt.

Kategorie tematyczne

• 47A58: Operator approximation theory
• 47A80: Tensor products of operators
• 47A75: Eigenvalue problems
• 46B50: Compactness in Banach (or normed) spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2013
• Tom: 214
• Numer: 3
• Strony: 265-278

Daty

wydano

2013

Twórcy

autor

David E. Edmunds

• Department of Mathematics, University of Sussex, Pevensey I, Brighton, BN1 9QH, United Kingdom

autor

Jan Lang

• Department of Mathematics, The Ohio State University, 100 Math Tower, 231 West 18th Avenue, Columbus, OH 43210-1174, U.S.A.

Identyfikatory

DOI

10.4064/sm214-3-5