Open AccessLinear maps determining the norm topology
Author(s) -
Krzysztof Jarosz
Publication year - 2000
Publication title -
transactions of the american mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.798
H-Index - 100
eISSN - 1088-6850
pISSN - 0002-9947
DOI - 10.1090/s0002-9947-00-02696-9
Subject(s) - algorithm , annotation , computer science , artificial intelligence
Let A A be a Banach function algebra on a compact space X X , and let a ∈ A a\in A be such that for any scalar λ \lambda the element a + λ e a+\lambda e is not a divisor of zero. We show that any complete norm topology on A A that makes the multiplication by a a continuous is automatically equivalent to the original norm topology of A A . Related results for general Banach spaces are also discussed.