| Title:
|
The Kadison problem on a class of commutative Banach algebras with closed cone (English) |
| Author:
|
Toumi, M. A. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
51 |
| Issue:
|
4 |
| Year:
|
2010 |
| Pages:
|
631-637 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The main result of the paper characterizes continuous local derivations on a class of commutative Banach algebra $A$ that all of its squares are positive and satisfying the following property: Every continuous bilinear map $\Phi $ from $A\times A$ into an arbitrary Banach space $B$ such that $\Phi(a,b)=0$ whenever $ab=0$, satisfies the condition $\Phi (ab,c)=\Phi(a,bc)$ for all $a,b,c\in A$. (English) |
| Keyword:
|
derivation |
| Keyword:
|
local derivation |
| MSC:
|
06F25 |
| MSC:
|
13N05 |
| MSC:
|
47B65 |
| idZBL:
|
Zbl 1224.06035 |
| idMR:
|
MR2858266 |
| . |
| Date available:
|
2010-11-30T16:24:03Z |
| Last updated:
|
2013-09-22 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140843 |
| . |
| Reference:
|
[1] Alaminos J., Brešar M., Cerne M., Extremera J., Villena A.R.: Zero product preserving maps on $C^{1}[0,1]$.J. Math. Anal. Appl. 347 (2008), 472–481. MR 2440343, 10.1016/j.jmaa.2008.06.037 |
| Reference:
|
[2] Alaminos J., Brešar M., Extremera J., Villena A.R.: Maps preserving zero products.Studia Math. 193 (2009), 131–159. MR 2515516, 10.4064/sm193-2-3 |
| Reference:
|
[3] Aliprantis C.D., Burkinshaw O.: Positive Operators.Academic Press, Orlando, 1985. Zbl 1098.47001, MR 0809372 |
| Reference:
|
[4] Buskes G., van Rooij A.: Almost $f$-algebras: commutativity and the Cauchy-Schwarz inequality.Positivity 4 (2000), 227–331. Zbl 0987.46002, MR 1797125, 10.1023/A:1009826510957 |
| Reference:
|
[5] Diem J.E.: A radical for lattice-ordered rings.Pacific J. Math. 25 (1968), 71–82. Zbl 0157.08004, MR 0227068, 10.2140/pjm.1968.25.71 |
| Reference:
|
[6] Kadison R.V.: Local derivations.J. Algebra 130 (1990), 494–509. Zbl 0751.46041, MR 1051316, 10.1016/0021-8693(90)90095-6 |
| Reference:
|
[7] Luxemburg W.A.J., Zaanen A.C.: Riesz Spaces I.North-Holland, Amsterdam, 1971. |
| Reference:
|
[8] De Pagter B.: f-algebras and orthomorphisms.Thesis, Leiden, 1981. |
| Reference:
|
[9] Schaefer H.H.: Banach lattices and positive operators.Springer, New York, 1974. Zbl 0296.47023, MR 0423039 |
| . |
