zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Biseparating linear maps between continuous vector-valued function spaces. (English) Zbl 1052.47017
The object of the paper under review is to present some vector-valued Banach-Stone theorems. Let X, Y be compact Hausdorff spaces, E and F two Banach spaces and C(X,E) the Banach space of all continuous E-valued functions defined on X. A linear map T:C(X,E)C(Y,F) is called separating if f(x)g(x)=0 for every xE implies that (Tf)(y)(Tg)(y)=0 for every yY. The authors show that every biseparating linear bijection T (that is, a T for which T and T -1 are separating) is a “weighted composition operator”. This means that there exists a function h of Y into the set of all bijective linear maps of E onto F and a homeomorphism ϕ from Y onto X such that Tf(y)=h(y)(f(ϕ(y)) for every fC(X,E) and yY. It is also shown that T is bounded if and only if for every yY, h(y) is a bounded linear operator from E onto F. An example of an unbounded T is given.
MSC:
47B33Composition operators
47B38Operators on function spaces (general)
46E40Spaces of vector- and operator-valued functions