[en] In this paper, we prove that if U is an increasing sequence of strictly positive and continuous functions on a locally compact Hausdorff space X such that VBAR congruent-to VBAR and C(X), then the Frechet space CU(X) is distinguished if and only if it satisfies Heinrich's density condition, or equivalently, if and only if the sequence U satisfies condition (H) (cf. e.g.`[1] for the introduction of (H)). As a consequence, the bidual lambda(infinity)(A) of the distinguished Kothe echelon space lambda-0(A) is distinguished if and only if the space lambda-1(A) is distinguished. This gives counterexamples to a problem of Grothendieck in the context of Kothe echelon spaces.
Disciplines :
Mathematics
Author, co-author :
Bastin, Françoise ; Université de Liège - ULiège > Département de mathématique > Analyse, analyse fonctionnelle, ondelettes
Language :
English
Title :
DISTINGUISHEDNESS OF WEIGHTED FRECHET SPACES OF CONTINUOUS-FUNCTIONS
Publication date :
1992
Journal title :
Proceedings of the Edinburgh Mathematical Society
ISSN :
0013-0915
eISSN :
1464-3839
Publisher :
Oxford Univ Press United Kingdom, Oxford, United Kingdom
scite shows how a scientific paper has been cited by providing the context of the citation, a classification describing whether it supports, mentions, or contrasts the cited claim, and a label indicating in which section the citation was made.
Bibliography
F. Bastin, Weighted spaces of continuous functions, Bull. Soc. Roy. Sci. Liège 1 (1990), 1–81.
K.-D. Bierstedt and J. Bonet, Stefan Heinrich's density condtion for Fréchet spaces and the characterization of the distinguished Kothe echelon spaces, Math. Nachr. 135 (1988), 149–180.
K.-D. Bierstedt and R. Meise, Distinguished echelon spaces and the projective description of the weighted inductive limits of type VC(X), in Aspects of Mathematics and its Applications (Elsevier Science Publ. B.V. North-Holland Math. Library, 1986).
K.-D. Bierstedt, R. Meise and W. Summers Kӧthe sets and Kӧthe sequence space, in Functional Analysis, Holomorphy and Approximation Theory (North-Holland Math. Studies 71, 1982), 27–91.
J. Bonet, S. Dierolf and C. Fernandez, The bidual of a distinguished Fréchet space need not be distinguished (1990), preprint.
D. Vogt, Distinguished Köthe spaces, Math. Z. 202 (1989), 143–146.
Similar publications
Sorry the service is unavailable at the moment. Please try again later.
This website uses cookies to improve user experience. Read more
Save & Close
Accept all
Decline all
Show detailsHide details
Cookie declaration
About cookies
Strictly necessary
Performance
Strictly necessary cookies allow core website functionality such as user login and account management. The website cannot be used properly without strictly necessary cookies.
This cookie is used by Cookie-Script.com service to remember visitor cookie consent preferences. It is necessary for Cookie-Script.com cookie banner to work properly.
Performance cookies are used to see how visitors use the website, eg. analytics cookies. Those cookies cannot be used to directly identify a certain visitor.
Used to store the attribution information, the referrer initially used to visit the website
Cookies are small text files that are placed on your computer by websites that you visit. Websites use cookies to help users navigate efficiently and perform certain functions. Cookies that are required for the website to operate properly are allowed to be set without your permission. All other cookies need to be approved before they can be set in the browser.
You can change your consent to cookie usage at any time on our Privacy Policy page.