# Strongly embedded subspaces of p-convex Banach function spaces

Strongly embedded subspaces of p-convex Banach function spaces Let $$X(\mu )$$ be a p-convex ( $$1\le p<\infty$$ ) order continuous Banach function space over a positive finite measure  $$\mu$$ . We characterize the subspaces of  $$X(\mu )$$ which can be found simultaneously in  $$X(\mu )$$ and a suitable $$L^1(\eta )$$ space, where $$\eta$$ is a positive finite measure related to the representation of  $$X(\mu )$$ as an $$L^p(m)$$ space of a vector measure  $$m$$ . We provide in this way new tools to analyze the strict singularity of the inclusion of  $$X(\mu )$$ in such an $$L^1$$ space. No rearrangement invariant type restrictions on  $$X(\mu )$$ are required. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals

# Strongly embedded subspaces of p-convex Banach function spaces

, Volume 17 (3) – Sep 13, 2012
17 pages

/lp/springer_journal/strongly-embedded-subspaces-of-p-convex-banach-function-spaces-OCJvJ0Q2k2
Publisher
Springer Journals
Subject
Mathematics; Fourier Analysis; Operator Theory; Potential Theory; Calculus of Variations and Optimal Control; Optimization; Econometrics
ISSN
1385-1292
eISSN
1572-9281
D.O.I.
10.1007/s11117-012-0204-6
Publisher site
See Article on Publisher Site

### Abstract

Let $$X(\mu )$$ be a p-convex ( $$1\le p<\infty$$ ) order continuous Banach function space over a positive finite measure  $$\mu$$ . We characterize the subspaces of  $$X(\mu )$$ which can be found simultaneously in  $$X(\mu )$$ and a suitable $$L^1(\eta )$$ space, where $$\eta$$ is a positive finite measure related to the representation of  $$X(\mu )$$ as an $$L^p(m)$$ space of a vector measure  $$m$$ . We provide in this way new tools to analyze the strict singularity of the inclusion of  $$X(\mu )$$ in such an $$L^1$$ space. No rearrangement invariant type restrictions on  $$X(\mu )$$ are required.

### Journal

PositivitySpringer Journals

Published: Sep 13, 2012

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