E-resources
-
Villena, A.R.
Journal of mathematical analysis and applications, 04/2017, Volume: 448, Issue: 1Journal Article
For a Banach function algebra A, we consider the problem of representing a continuous d-homogeneous polynomial P:A→X, where X is an arbitrary Banach space, that satisfies the property P(f+g)=P(f)+P(g) whenever f,g∈A are such that supp(f)∩supp(g)=∅. We show that such a polynomial can be represented as P(f)=T(fd)(f∈A) for some continuous linear map T:A→X for a variety of Banach function algebras such as the algebra of continuous functions C0(Ω) for any locally compact Hausdorff space Ω, the algebra of Lipschitz functions lipα(K) for any compact metric space K and α∈0,1, the Figà–Talamanca–Herz algebra Ap(G) for some locally compact groups G and p∈1,+∞, the algebras AC(a,b) and BVC(a,b) of absolutely continuous functions and of continuous functions of bounded variation on the interval a,b. In the case where A=Cn(a,b), P can be represented as P(f)=∑T(n1,…,nd)(f(n1)⋯f(nd)), where the sum is taken over (n1,…,nd)∈Zd with 0≤n1≤…≤nd≤n, for appropriate continuous linear maps T(n1,…,nd):Cn−nd(a,b)→X.
Author
Shelf entry
Permalink
- URL:
Impact factor
Access to the JCR database is permitted only to users from Slovenia. Your current IP address is not on the list of IP addresses with access permission, and authentication with the relevant AAI accout is required.
Year | Impact factor | Edition | Category | Classification | ||||
---|---|---|---|---|---|---|---|---|
JCR | SNIP | JCR | SNIP | JCR | SNIP | JCR | SNIP |
Select the library membership card:
If the library membership card is not in the list,
add a new one.
DRS, in which the journal is indexed
Database name | Field | Year |
---|
Links to authors' personal bibliographies | Links to information on researchers in the SICRIS system |
---|
Source: Personal bibliographies
and: SICRIS
The material is available in full text. If you wish to order the material anyway, click the Continue button.