Wyniki wyszukiwania

Sortuj według:

Ogranicz wyniki do:

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

100%

Edmunds D., Lang J.

Studia Mathematica

2013

tom 214

nr 3

265-278

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.

Artykuł dostępny w postaci pełnego tekstu - kliknij by otworzyć plik

Series representation of compact linear operators in Banach spaces

100%

Edmunds D. E., Lang J.

Commentationes Mathematicae

2016

tom 56

nr 1

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.

Ograniczanie wyników

1 Commentationes Mathematicae

1 Studia Mathematica

2 Lang J.

1 Edmunds D.

1 Edmunds D. E.

1 2016

1 2013

Wyniki wyszukiwania

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

Series representation of compact linear operators in Banach spaces