Wyniki wyszukiwania

Sortuj według:

Ogranicz wyniki do:

Compactness properties of the integration mapassociated with a vector measure

100%

Okada S., Ricker W. J.

Colloquium Mathematicum

1993

tom 66

nr 2

175-185

Operator ideal properties of vector measures with finite variation

81%

Okada S., Ricker W., Rodríguez-Piazza L.

Studia Mathematica

2011

tom 205

nr 3

215-249

Given a vector measure m with values in a Banach space X, a desirable property (when available) of the associated Banach function space L¹(m) of all m-integrable functions is that L¹(m) = L¹(|m|), where |m| is the [0,∞]-valued variation measure of m. Closely connected to m is its X-valued integration map Iₘ: f ↦ ∫f dm for f ∈ L¹(m). Many traditional operators from analysis arise as integration maps in this way. A detailed study is made of the connection between the property L¹(m) = L¹(|m|) and the membership of Iₘ in various classical operator ideals(e.g., the compact, p-summing, completely continuous operators). Depending on which operator ideal is under consideration, the geometric nature of the Banach space X may also play a crucial role. Of particular importance in this regard is whether or not X contains an isomorphic copy of the classical sequence space ℓ¹. The compact range property of X is also relevant.

Ograniczanie wyników

1 Colloquium Mathematicum

1 Studia Mathematica

2 Okada S.

1 Ricker W.

1 Ricker W. J.

1 Rodríguez-Piazza L.

1 2011

1 1993

Wyniki wyszukiwania

Compactness properties of the integration mapassociated with a vector measure

Operator ideal properties of vector measures with finite variation