Open AccessRelative boundedness and relative compactness for linear operators in Banach spaces
Author(s) -
Paul Binding,
Rostyslav Hryniv
Publication year - 2000
Publication title -
proceedings of the american mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.968
H-Index - 84
eISSN - 1088-6826
pISSN - 0002-9939
DOI - 10.1090/s0002-9939-00-05729-4
Subject(s) - annotation , algorithm , computer science , type (biology) , semantics (computer science) , artificial intelligence , programming language , biology , ecology
If A A and B B are linear operators acting between Banach spaces, we show that compactness of B B relative to A A does not in general imply that B B has A A -bound zero. We do, however, give conditions under which the above implication is valid.