Characterizations of Sunduals (Summary)

Characterizations of Sunduals (Summary) Positivity 7: 81–85, 2003. © 2003 Kluwer Academic Publishers. Printed in the Netherlands. W.A.J. LUXEMBURG Department of Mathematics, 253–37, California Institute of Technology, Pasadena, CA 91125-003, USA. E-mail: 1. Let G ={T(t) : t  0} be a C -semigroup of bounded linear operators, acting on a real or complex Banach space E, i.e., T(0) = I , the identity operator; (∀t, s 0)(T (t +s) = T(t)T (s)); and the mapping t → T(t) of R := {t ∈ R : t  0} into L(E) the Banach algebra of all bounded linear operators acting on E is strongly continuous (in this context “C " means continuous at 0). ∗ ∗ The dual semigroup G := {T (t ) : t  0}, defines a semigroup of bounded linear operators on the Banach dual space E of E.If E is not reflexive, then G need not be strongly continuous. By its very definition, however, the mapping ∗ ∗ t → T (t ) of R into L(E ) is a weak-∗-continuous semigroup of bounded and weak-∗-continuous linear operators of E . For example, let E = C (R), the space of the continuous functions on R vanishing Positivity Springer Journals

Characterizations of Sunduals (Summary)

Loading next page...
Kluwer Academic Publishers
Copyright © 2003 by Kluwer Academic Publishers
Mathematics; Fourier Analysis; Operator Theory; Potential Theory; Calculus of Variations and Optimal Control; Optimization; Econometrics
Publisher site
See Article on Publisher Site


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


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.



billed annually
Start Free Trial

14-day Free Trial