Search

Start Over Subject tensor product

1. $w^*$-basic sequences and reflexivity of Banach spaces

Creator:
John, Kamil
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
reflexive Banach space, Schauder basis, quotient space, w$^*$-basic sequence, and tensor product
Language:
English
Description:
We observe that a separable Banach space $X$ is reflexive iff each of its quotients with Schauder basis is reflexive. Similarly if $\mathcal L(X,Y)$ is not reflexive for reflexive $X$ and $Y$ then $\mathcal L(X_1, Y)$ is is not reflexive for some $X_1\subset X$, $X_1$ having a basis.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

2. On fuzzification of the notion of quantaloid

Creator:
Solovyov, Sergey A.
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
many-value topology, monadic category, nucleus, quantale, quantale algebra, quantale algebroid, quantale module, quantaloid, and tensor product
Language:
English
Description:
The paper considers a fuzzification of the notion of quantaloid of K. I. Rosenthal, which replaces enrichment in the category of ⋁-semilattices with that in the category of modules over a given unital commutative quantale. The resulting structures are called quantale algebroids. We show that their constitute a monadic category and prove a representation theorem for them using the notion of nucleus adjusted for our needs. We also characterize the lattice of nuclei on a free quantale algebroid. At the end of the paper, we prove that the category of quantale algebroids has a monoidal structure given by tensor product.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

3. The Grothendieck property for injective tensor products of Banach spaces

Creator:
Ji, Donghai, Xue, Xiaoping, and Bu, Qingying
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
Banach space, Grothendieck property, and tensor product
Language:
English
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.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public