Advanced Search

Query:

Fill in the form and click »Search«...

Format:

Display: entries per page entries

Zbl 0805.46049
Font, J.J.; Hernandez, S.
On separating maps between locally compact spaces. (English)
[J] Arch. Math. 63, No.2, 158-165 (1994). ISSN 0003-889X; ISSN 1420-8938/e

A linear map $H$ defined from a subalgebra $A$ of $C\sb 0(T)$ into a subalgebra $B$ of $C\sb 0(S)$ is said to be separating or disjointness preserving if $x\cdot y\equiv 0$ implies $Hx\cdot Hy\equiv 0$ for all $x,y\in A$.\par The authors show that a separating bijection $H$ is automatically continuous (indeed, a weighted composition map) and induces a homeomorphism between the locally compact spaces $T$ and $S$.\par If $A$ and $B$ are the continuous functions on $T$ and $S$, respectively, with compact support, then a similar result for a separating injection is obtained. This result is applied to generalize to functions with compact support a well-kown theorem by Holsztyński about linear into isometries between $C(T)$ and $C(S)$ with $T$ and $S$ compact spaces.
[J.J.Font (Castellón)]

MSC 2000:: *46H40 Automatic continuity
46J10 Banach algebras of continuous functions
47B38 Operators on function spaces

Keywords: disjointness preserving or separating map; Banach-Stone theorem; separating bijection; automatically continuous; weighted composition map

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Advanced Search

Zentralblatt MATH Berlin [Germany]