Vol. 26, No. 2, 1968

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 304: 1  2
Vol. 303: 1  2
Vol. 302: 1  2
Vol. 301: 1  2
Vol. 300: 1  2
Vol. 299: 1  2
Vol. 298: 1  2
Vol. 297: 1  2
Online Archive
Volume:
Issue:
     
The Journal
Editorial Board
Subscriptions
Officers
Special Issues
Submission Guidelines
Submission Form
Contacts
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Author Index
To Appear
 
Other MSP Journals
Bounded generators of linear spaces

Takashi Ito and Thomas I. Seidman

Vol. 26 (1968), No. 2, 283–287
Abstract

Let Sφ = {x X : supαφα(x) < ∞} where φ = {φα} is a family of semi-norms determining the topology of X. It is shown that φ may be chosen so Sφ is dense if and only if X has a bounded generating set if and only if there is a continuous norm on X. It is shown that these conditions hold for separable Fréchet spaces and for quotients of products of Banach spaces. An example is given of a Fréchet space containing no bounded generating set thus contradicting an assertion of L. Maté that Sφ is dense for Fréchet spaces.

Mathematical Subject Classification
Primary: 46.01
Milestones
Received: 26 July 1967
Published: 1 August 1968
Authors
Takashi Ito
Thomas I. Seidman