Abstract.In this note, we introduce the study of special sets in the range of certain surjective mappings. The points in these sets have the property that ``nearby" points have preimages that are forced to be large in norm. For multilinear operators, these points illustrate how it is possible to not be open at the origin, despite being surjective. We also give a type of Open Mapping Theorem for surjective multilinear operators whose range has small dimension, and a corollary concerning right inverses.

Received: June 28, 2006

AMS Subject Classification: 46T99

Key Words and Phrases: open, bilinear, surjective, onto, repelling

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2006
Volume: 30
Issue: 4