| Title:
|
On the Lipschitz operator algebras (English) |
| Author:
|
Ebadian, A. |
| Author:
|
Shokri, A. A. |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
45 |
| Issue:
|
3 |
| Year:
|
2009 |
| Pages:
|
213-222 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In a recent paper by H. X. Cao, J. H. Zhang and Z. B. Xu an $\alpha $-Lipschitz operator from a compact metric space into a Banach space $A$ is defined and characterized in a natural way in the sence that $F:K\rightarrow A$ is a $\alpha $-Lipschitz operator if and only if for each $\sigma \in X^*$ the mapping $\sigma \circ F$ is a $\alpha $-Lipschitz function. The Lipschitz operators algebras $L^\alpha (K,A)$ and $l^\alpha (K,A)$ are developed here further, and we study their amenability and weak amenability of these algebras. Moreover, we prove an interesting result that $L^\alpha (K,A)$ and $l^\alpha (K,A)$ are isometrically isomorphic to $L^{\alpha }(K)\check{\otimes }A$ and $l^{\alpha }(K)\check{\otimes }A$ respectively. Also we study homomorphisms on the $L^\alpha _A(X,B)$. (English) |
| Keyword:
|
Lipschitz algebras |
| Keyword:
|
amenability |
| Keyword:
|
homomorphism |
| MSC:
|
46H25 |
| MSC:
|
46J10 |
| MSC:
|
47B48 |
| idZBL:
|
Zbl 1211.47074 |
| idMR:
|
MR2591677 |
| . |
| Date available:
|
2009-09-18T11:25:08Z |
| Last updated:
|
2013-09-19 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134233 |
| . |
| Reference:
|
[1] Alimohammadi, D., Ebadian, A.: Headberg’s theorem in real Lipschitz algebras.Indian J. Pure Appl. Math. 32 (2001), 1479–1493. MR 1878062 |
| Reference:
|
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| Reference:
|
[3] Cao, H. X., Xu, Z. B.: Some properties of Lipschitz-$\alpha $ operators.Acta Math. Sin. (Engl. Ser.) 45 (2) (2002), 279–286. MR 1928136 |
| Reference:
|
[4] Cao, H. X., Zhang, J. H., Xu, Z. B.: Characterizations and extentions of Lipschitz-$\alpha $ operators.Acta Math. Sin. (Engl. Ser.) 22 (3) (2006), 671–678. MR 2219676, 10.1007/s10114-005-0727-x |
| Reference:
|
[5] Dales, H. G.: Banach Algebras and Automatic Continuty.Clarendon Press, Oxford, 2000. MR 1816726 |
| Reference:
|
[6] Ebadian, A.: Prime ideals in Lipschitz algebras of finite differentable function.Honam Math. J. 22 (2000), 21–30. MR 1779197 |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
[10] Runde, V.: Lectures on Amenability.Springer, 2001. MR 1874893 |
| Reference:
|
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| Reference:
|
[12] Sherbert, D. R.: The structure of ideals and point derivations in Banach algebras of Lipschitz functions.Trans. Amer. Math. Soc. 111 (1964), 240–272. Zbl 0121.10204, MR 0161177, 10.1090/S0002-9947-1964-0161177-1 |
| Reference:
|
[13] Weaver, N.: Subalgebras of little Lipschitz algebras.Pacific J. Math. 173 (1996), 283–293. Zbl 0846.54013, MR 1387803 |
| Reference:
|
[14] Weaver, N.: Lipschitz Algebras.World Scientific Publishing Co., Inc., River Edge, NJ, 1999. Zbl 0936.46002, MR 1832645 |
| . |
