| Title:
|
Locally m-pseudoconvex topologies on locally A-pseudoconvex algebras (English) |
| Author:
|
Abel, M. |
| Author:
|
Arhippainen, J. |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
54 |
| Issue:
|
3 |
| Year:
|
2004 |
| Pages:
|
675-680 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $(A, T )$ be a locally A-pseudoconvex algebra over $\mathbb{R}$ or $\mathbb{C}$. We define a new topology $m (T)$ on $A$ which is the weakest among all m-pseudoconvex topologies on $A$ stronger than $T$. We describe a family of non-homogeneous seminorms on $A$ which defines the topology $m(T)$. (English) |
| Keyword:
|
locally A-pseudoconvex algebra |
| Keyword:
|
locally m-pseudoconvex algebra |
| MSC:
|
46H05 |
| MSC:
|
46H20 |
| idZBL:
|
Zbl 1080.46518 |
| idMR:
|
MR2086724 |
| . |
| Date available:
|
2009-09-24T11:16:22Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127919 |
| . |
| Reference:
|
[1] M. Abel: Gelfand-Mazur Algebras, Topological Vector Spaces, Algebras and Related Areas (Hamilton, ON).Pitman Research Notes in Math. Series 316, Longman Scientific & Technical, London, 1994, pp. 116–129. MR 1319378 |
| Reference:
|
[2] M. Abel and A. Kokk: Locally pseudoconvex Gelfand-Mazur algebras.Eesti Tead. Akad. Toimetised Füüs.-Mat. 37, 377–386. (Russian) MR 0985621 |
| Reference:
|
[3] J. Arhippainen: On functional representation of uniformly A-convex algebras.Math. Japon. 46 (1997), 509–515. Zbl 0896.46036, MR 1487302 |
| Reference:
|
[4] J. Arhippainen: On functional representation of commutative locally A-convex algebras.Rocky Mountain J. Math. 30 (2000), 777–794. Zbl 1052.46037, MR 1797813, 10.1216/rmjm/1021477242 |
| Reference:
|
[5] A. C. Cochran: Topological algebras and Mackey topologies.Proc. Amer. Math. Soc. 30 (1971), 115–119. Zbl 0219.46036, MR 0291807, 10.1090/S0002-9939-1971-0291807-4 |
| Reference:
|
[6] A. C. Cochran: Representation of A-convex algebras.Proc. Amer. Math. Soc. 41 (1973), 473–479. Zbl 0272.46029, MR 0333735 |
| Reference:
|
[7] A. C. Cochran, R. Keown and C. R. Williams: On class of topological algebras.Pacific J. Math. 34 (1970), 17–25. MR 0273399, 10.2140/pjm.1970.34.17 |
| Reference:
|
[8] T. Husain: The Open Mapping and Closed Graph Theorems in Topological Vector Spaces.Clarendon Press, Oxford, 1965. Zbl 0124.06301, MR 0178331 |
| Reference:
|
[9] L. Oubbi: Topologies m-convexes dans les algebres A-convexes.Rend. Circ. Mat. Palermo XLI (1992), 397–406. Zbl 0798.46043, MR 1230587 |
| Reference:
|
[10] L. Oubbi: Representation of locally convex algebras.Rev. Mat. Univ. Complut. Madrid 35 (1994), 233–244. Zbl 0820.46047, MR 1297513 |
| Reference:
|
[11] M. Oudadess: Unité et semi-normes dans les algèbres localement convexes.Rev. Colombiana Mat. 16 (1982), 141–150. Zbl 0565.46028, MR 0685249 |
| Reference:
|
[12] T. W. Palmer: Banach Algebras and the General Theory of $^\ast $-Algebras.Cambridge Univ. Press, New York, 1994. Zbl 0809.46052 |
| Reference:
|
[13] L. Waelbroeck: Topological Vector Spaces and Algebras. Lecture Notes in Math. 230.Springer-Verlag, Berlin-New York, 1971. MR 0467234 |
| . |
