Maps preserving common zeros between subspaces of vector-valued continuous functions

Maps preserving common zeros between subspaces of vector-valued continuous functions For metric spaces X and Y, normed spaces E and F, and certain subspaces A(X, E) and A(Y, F) of vector-valued continuous functions, we obtain a complete characterization of linear and bijective maps $${T:A(X,E)\rightarrow A(Y,F)}$$ preserving common zeros, that is, maps satisfying the property $$Z(f) \cap Z(g) \neq \emptyset \Longleftrightarrow Z(Tf) \cap Z(Tg) \neq \emptyset \quad\quad\quad{\rm (P)}$$ for any $${f, g \in A(X, E)}$$ , where $${Z(f) = \{x \in X: f(x) = 0\}}$$ . Moreover, we provide some examples of subspaces for which the automatic continuity of linear bijections having the property (P) is derived. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals

Maps preserving common zeros between subspaces of vector-valued continuous functions

, Volume 14 (4) – Feb 9, 2010
9 pages

/lp/springer_journal/maps-preserving-common-zeros-between-subspaces-of-vector-valued-Lf68c100ct
Publisher
SP Birkhäuser Verlag Basel
Subject
Mathematics; Econometrics; Calculus of Variations and Optimal Control; Optimization; Potential Theory; Operator Theory; Fourier Analysis
ISSN
1385-1292
eISSN
1572-9281
D.O.I.
10.1007/s11117-010-0046-z
Publisher site
See Article on Publisher Site

DeepDyve is your personal research library

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

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. 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

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

14-day Free Trial