The Grothendieck property for injective tensor products of Banach spaces

Title:

The Grothendieck property for injective tensor products of Banach spaces

Creator:

Ji, Donghai, Xue, Xiaoping, and Bu, Qingying

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:14da489d-609f-4c47-ac57-6787c79a0c83
uuid:14da489d-609f-4c47-ac57-6787c79a0c83

Subject:

Banach space, Grothendieck property, and tensor product

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

Let $X$ be a Banach space with the Grothendieck property, $Y$ a reflexive Banach space, and let $X\check{\otimes}_{\varepsilon} Y$ be the injective tensor product of $X$ and $Y$. \item {(a)} If either $X^{\ast \ast }$ or $Y$ has the approximation property and each continuous linear operator from $X^\ast $ to $Y$ is compact, then $X\check{\otimes}_{\varepsilon} Y$ has the Grothendieck property. \item {(b)} In addition, if $Y$ has an unconditional finite dimensional decomposition, then $X\check{\otimes}_{\varepsilon} Y$ has the Grothendieck property if and only if each continuous linear operator from $X^\ast $ to $Y$ is compact.

Language:

English

Rights:

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

Coverage:

1153-1159

Source:

Czechoslovak Mathematical Journal | 2010 Volume:60 | Number:4

Harvested from:

CDK

Metadata only:

false