On $p$-convexification of the Banach-Kantorovich lattice
Let $B$ be a complete Boolean algebra, $Q(B)$ the Stone compact of $B$, and let $C_\infty (Q(B))$ be the commutative unital algebra of all continuous functions $x: Q(B) \to [-\infty, +\infty]$, assuming possibly the values $\pm\infty$ on nowhere-dense subsets of $Q(B)$. Let $(E,\|\cdot\|_{E}) \sub...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
EJAAM
2024-12-01
|
| Series: | E-Journal of Analysis and Applied Mathematics |
| Subjects: | |
| Online Access: | https://ejaam.org/articles/2024/10.62780-ejaam-2024-004.pdf |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | Let $B$ be a complete Boolean algebra, $Q(B)$ the Stone compact of $B$, and let $C_\infty (Q(B))$ be the commutative unital algebra of all continuous functions $x: Q(B) \to [-\infty, +\infty]$, assuming possibly the values $\pm\infty$ on nowhere-dense subsets of $Q(B)$. Let $(E,\|\cdot\|_{E}) \subset C_\infty (Q(B))$ be a Banach-Kantorovich lattice over the algebra $L^0(\Omega)$ of equivalence classes of almost everywhere finite real-valued measurable functions on a measurable space $(\Omega, \Sigma, \mu)$ with $\sigma$-finite measure $\mu$. The paper defines the $p$-convexification of the Banach-Kantorovich lattice $(E,\|\cdot\|_{E})$ and proves that it is also a Banach-Kantorovich lattice over $L^0(\Omega)$. |
|---|---|
| ISSN: | 2544-9990 |