$$f$$ f -Representation of a function algebra

$$f$$ f -Representation of a function algebra We investigate representations $$\Phi :A\longrightarrow \mathcal {L}_{b}(X)$$ Φ : A ⟶ L b ( X ) , where $$A$$ A is a unital function algebra and $$\mathcal {L}_{b}(X)$$ L b ( X ) is the space of all order bounded operators on a vector lattice $$X$$ X . Given an element $$x\in X$$ x ∈ X , the orbit space $$\Phi \left[ x\right] $$ Φ x generated by $$\Phi $$ Φ at $$x$$ x is the subspace $$\begin{aligned} \Phi \left[ x\right] =\left\{ \Phi (a)(x):a\in A\right\} . \end{aligned}$$ Φ x = Φ ( a ) ( x ) : a ∈ A . In this paper we make a detailed study of the orbite space $$\Phi \left[ x\right] , x\in X$$ Φ x , x ∈ X . It turn out that they are vector lattices with a weak order unit. Moreover, It is proved that for any representation $$\Phi :A\longrightarrow \mathcal {L}_{b}(X)$$ Φ : A ⟶ L b ( X ) can be extended to a representation of the order bidual $$A^{\sim }{}^{\sim }$$ A ∼ ∼ of $$A$$ A . http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals

$$f$$ f -Representation of a function algebra

Positivity , Volume 19 (4) – Jan 29, 2015

Loading next page...
 
/lp/springer_journal/f-f-representation-of-a-function-algebra-XP6I3vKBfb
Publisher
Springer Basel
Copyright
Copyright © 2015 by Springer Basel
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/s11117-015-0325-9
Publisher site
See Article on Publisher Site

References

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
discover and read the research
that matters to you.

Enjoy affordable access to
over 12 million articles from more than
10,000 peer-reviewed journals.

All for just $49/month

Explore the DeepDyve Library

Unlimited reading

Read as many articles as you need. Full articles with original layout, charts and figures. Read online, from anywhere.

Stay up to date

Keep up with your field with Personalized Recommendations and Follow Journals to get automatic updates.

Organize your research

It’s easy to organize your research with our built-in tools.

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.

See the journals in your area

Monthly Plan

  • Read unlimited articles
  • Personalized recommendations
  • No expiration
  • Print 20 pages per month
  • 20% off on PDF purchases
  • Organize your research
  • Get updates on your journals and topic searches

$49/month

Start Free Trial

14-day Free Trial

Best Deal — 39% off

Annual Plan

  • All the features of the Professional Plan, but for 39% off!
  • Billed annually
  • No expiration
  • For the normal price of 10 articles elsewhere, you get one full year of unlimited access to articles.

$588

$360/year

billed annually
Start Free Trial

14-day Free Trial