Relative boundedness and relative compactness for linear operators in Banach spaces

Authors
Binding, P Hryniv, R
Citation
P. Binding et R. Hryniv, Relative boundedness and relative compactness for linear operators in Banach spaces, P AM MATH S, 128(8), 2000, pp. 2287-2290
Citations number
7
Categorie Soggetti
Mathematics
Journal title
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
ISSN journal
00029939 → ACNP
Volume
128
Issue
8
Year of publication
2000
Pages
2287 - 2290
Database
ISI
SICI code
0002-9939(2000)128:8<2287:RBARCF>2.0.ZU;2-W
Abstract
If A and B are linear operators acting between Banach spaces, we show that compactness of B relative to A does not in general imply that B has A-bound zero. We do, however, give conditions under which the above implication is valid.