# Positive Representations of L 1 of a Vector Measure

Positive Representations of L 1 of a Vector Measure We characterize the vector measures n on a Banach lattice such that the map $$\|\int|\cdot|dn \|$$ provides a quasi-norm which is equivalent to the canonical norm $$\|\cdot\|_{n}$$ of the space L 1(n) of integrable functions as an specific type of transformations of positive vector measures that we call cone-open transformations. We also prove that a vector measure m on a Banach space X constructed as a cone-open transformation of a positive vector measure can be considered in some sense as a positive vector measure by defining a new order on X. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals

# Positive Representations of L 1 of a Vector Measure

11 pages

1

/lp/springer_journal/positive-representations-of-l-1-of-a-vector-measure-TGJey8WSNF
Publisher site
See Article on Publisher Site

### Abstract

We characterize the vector measures n on a Banach lattice such that the map $$\|\int|\cdot|dn \|$$ provides a quasi-norm which is equivalent to the canonical norm $$\|\cdot\|_{n}$$ of the space L 1(n) of integrable functions as an specific type of transformations of positive vector measures that we call cone-open transformations. We also prove that a vector measure m on a Banach space X constructed as a cone-open transformation of a positive vector measure can be considered in some sense as a positive vector measure by defining a new order on X.

### Journal

PositivitySpringer Journals

Published: Jan 1, 2007

## You’re reading a free preview. Subscribe to read the entire article.

### DeepDyve is your personal research library

It’s your single place to instantly
that matters to you.

over 18 million articles from more than
15,000 peer-reviewed journals.

All for just $49/month ### Explore the DeepDyve Library ### Search Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly ### Organize Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place. ### Access Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals. ### Your journals are on DeepDyve Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more. All the latest content is available, no embargo periods. DeepDyve ### Freelancer DeepDyve ### Pro Price FREE$49/month
\$360/year

Save searches from
PubMed

Create folders to

Export folders, citations