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)
Disjointness preserving mappings between Fourier algebras. (English) Zbl 0911.43003
Let G be a locally compact group. The Fourier-Stieltjes algebra B(G) and the Fourier algebra A(G) were for the first time investigated by P. Eymard in 1964. The paper proves mainly that for two locally compact amenable groups G 1 and G 2 , the Fourier algebras A(G 1 ) and A(G 2 ) are algebra isomorphic if and only if there exists a disjointness preserving bijection between them (Theorem 4), and such disjointness preserving bijection of A(G 1 ) onto A(G 2 ) can be extended, in a unique way, to a weighted composition bijection of B(G 1 ) onto B(G 2 ) (Theorem 5). The author notices that if the amenability of the group G is dropped, these results may fail to be true. The following may be an interesting question (like the inverse problem of the paper): can an isometric isomorphism or a bipositive algebra isomorphism between A(G 1 ) and A(G 2 ) (or B(G 1 ) and B(G 2 )) be deduced to a topological isomorphism of G 1 onto G 2 ?
MSC:
43A30Fourier and Fourier-Stieltjes transforms on nonabelian groups and on semigroups, etc.
43A15L p -spaces and other function spaces on groups, semigroups, etc.
47B48Operators on Banach algebras