On coincidence of Pettis and McShane integrability

Title:

On coincidence of Pettis and McShane integrability

Creator:

Fabian, Marián

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:f6e8a427-0550-4a0e-ae77-b546263b5c6e
uuid:f6e8a427-0550-4a0e-ae77-b546263b5c6e

Subject:

Pettis integral, McShane integral, MC-filling family, uniform Eberlein compact space, scalarly negligible function, Lebesgue injection, Hilbert generated space, strong Markuševič basis, and adequate inflation

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

R. Deville and J. Rodríguez proved that, for every Hilbert generated space $X$, every Pettis integrable function $f\colon [0,1]\rightarrow X$ is McShane integrable. R. Avilés, G. Plebanek, and J. Rodríguez constructed a weakly compactly generated Banach space $X$ and a scalarly null (hence Pettis integrable) function from $[0,1]$ into $X$, which was not McShane integrable. We study here the mechanism behind the McShane integrability of scalarly negligible functions from $[0,1]$ (mostly) into $C(K)$ spaces. We focus in more detail on the behavior of several concrete Eberlein (Corson) compact spaces $K$, that are not uniform Eberlein, with respect to the integrability of some natural scalarly negligible functions from $[0,1]$ into $C(K)$ in McShane sense.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

83-106

Source:

Czechoslovak Mathematical Journal | 2015 Volume:65 | Number:1

Harvested from:

CDK

Metadata only:

false