zbMATH — the first resource for mathematics

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.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
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)
Pseudo-characters and almost multiplicative functionals. (English) Zbl 0958.43001
The main subject studied in the paper under review is the so called stable approximability of the set of characters or continuous characters on a group, i.e. the question whether they can uniformly on $G$ approximate every almost character. Theorem 1 asserts that on an amenable locally compact group every measurable $\varepsilon$-character can uniformly be approximated on $G$ by continuous characters. The logarithms of multiplicative pseudo-characters can be chosen to be some real additive almost characters (Theorem 2) and in Theorem 3 the author shows that the involutive Banach group algebra $\ell_1(G)$ is an AMNM (i.e. “algebra on which almost multiplicative functionals are near to multiplicative functionals”) if and only if the set of characters on $G$ is stable.

43A07Means on groups, semigroups, etc.; amenable groups
Full Text: DOI
[1] Banach, S.; Tarski, A.: Sur la décomposition des ensembles de points en parties respectivement congruentes. Fund. math. 6, 244-277 (1924) · Zbl 50.0370.02
[2] Cenzer, D.: The stability problem for transformations of the circle. Proc. roy. Soc. Edinburgh sect. A 84, 279-281 (1979) · Zbl 0439.39004
[3] Cenzer, D.: The stability problem: new results and counterexamples. Lett. math. Phys. 10, 155-160 (1985) · Zbl 0595.39010
[4] Forti, G. L.: The stability of homomorphisms and amenability, with applications to functional equations. Abh. math. Sem. univ. Hamburg 57, 215-226 (1987) · Zbl 0619.39012
[5] Forti, G. L.: Hyers--Ulam stability of functional equations in several variables. Aequationes math. 50, 143-190 (1995) · Zbl 0836.39007
[6] Gelbaum, B. R.; Olmstead, J. M. H.: Theorems and counterexamples in mathematics. Problem books in math. (1990)
[7] Greenleaf, F. P.: Invariant means on topological groups. Van nostrand mathematical studies 16 (1969) · Zbl 0174.19001
[8] Grove, K.; Karcher, H.; Roh, E. A.: Jacobi fields and Finsler metrics on compact Lie groups with an application to differentiable pinching problems. Math. ann. 211, 7-21 (1974) · Zbl 0273.53051
[9] De La Harpe, P.; Karoubi, M.: Representations approchées d’un groupe dans une algèbre de Banach. Manuscripta math. 22, 293-310 (1977) · Zbl 0371.22007
[10] Hyers, D. H.; Rassias, Th.M.: Approximate homomorphisms. Aequationes math. 44, 125-153 (1992) · Zbl 0806.47056
[11] Jarosz, K.: Perturbations of Banach algebras. Springer lecture notes in mathematics 1120 (1985) · Zbl 0557.46029
[12] Johnson, B. E.: Approximately multiplicative functionals. J. London math. Soc. 34, 489-510 (1986) · Zbl 0625.46059
[13] Johnson, B. E.: Approximately multiplicative maps between Banach algebras. J. London math. Soc. 37, 294-316 (1988) · Zbl 0652.46031
[14] Johnson, B. E.: Cohomology in Banach algebras. Memoirs AMS 127 (1972) · Zbl 0256.18014
[15] Kazhdan, D.: On ${\epsilon}$-representations. Israel J. Math. 43, 315-323 (1982) · Zbl 0518.22008
[16] Ore, O.: Some remarks on commutators. Proc. amer. Math. soc. 2, 307-314 (1951) · Zbl 0043.02402
[17] Pełczyński, A.: Linear extensions, linear averagings, and their applications to linear topological classification of spaces of continuous functions. Dissertationes math. 58 (1968) · Zbl 0165.14603
[18] Rudin, W.: Análisis real y complejo. (1979)
[19] Shtern, A. I.: Quasirepresentations and pseudorepresentations. Funkt. anal. Prilozhen. 25, 70-73 (1991) · Zbl 0737.22003
[20] Székelyhidi, L.: Note on a stability theorem. Canad. math. Bull. 25, 500-501 (1982) · Zbl 0505.39002
[21] Ulam, S. M.: A collection of mathematical problems. (1960) · Zbl 0086.24101
[22] Ulam, S. M.: Problems in modern mathematics. (1964) · Zbl 0137.24201
[23] Ulam, S. M.: Set, numbers and universes. (1974) · Zbl 0558.00017
[24] Ulam, S. M.: An anecdotal history of the scottish book. The scottish book (1981)