Some properties and applications of equicompact sets of operators

• Autorzy: E. Serrano , C. Piñeiro , J. M. Delgado
• Języki publikacji: EN

Abstrakty

EN

Let X and Y be Banach spaces. A subset M of 𝓚(X,Y) (the vector space of all compact operators from X into Y endowed with the operator norm) is said to be equicompact if every bounded sequence (xₙ) in X has a subsequence $(x_{k(n)})ₙ$ such that $(Tx_{k(n)})ₙ$ is uniformly convergent for T ∈ M. We study the relationship between this concept and the notion of uniformly completely continuous set and give some applications. Among other results, we obtain a generalization of the classical Ascoli theorem and a compactness criterion in $ℳ_{c}(ℱ,X)$, the Banach space of all (finitely additive) vector measures (with compact range) from a field ℱ of sets into X endowed with the semivariation norm.

Kategorie tematyczne

• 47B07: Operators defined by compactness properties
• 46G10: Vector-valued measures and integration

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2007
• Tom: 181
• Numer: 2
• Strony: 171-180

Daty

wydano

2007

Twórcy

autor

E. Serrano

• Departamento de Matemáticas, Facultad de Ciencias Experimentales, Campus Universitario del Carmen, Avda. de las Fuerzas Armadas s/n, E-21071 Huelva, Spain

autor

C. Piñeiro

• Departamento de Matemáticas, Facultad de Ciencias Experimentales, Campus Universitario del Carmen, Avda. de las Fuerzas Armadas s/n, E-21071 Huelva, Spain

autor

J. M. Delgado

• Departamento de Matemáticas, Facultad de Ciencias Experimentales, Campus Universitario del Carmen, Avda. de las Fuerzas Armadas s/n, E-21071 Huelva, Spain

Identyfikatory

DOI

10.4064/sm181-2-4