| Title:
|
Totally convex algebras (English) |
| Author:
|
Pumplün, Dieter |
| Author:
|
Röhrl, Helmut |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
33 |
| Issue:
|
2 |
| Year:
|
1992 |
| Pages:
|
205-235 |
| . |
| Category:
|
math |
| . |
| Summary:
|
By definition a totally convex algebra $A$ is a totally convex space $|A|$ equipped with an associative multiplication, i.e\. a morphism $\mu :|A|\otimes |A|\longrightarrow |A|$ of totally convex spaces. In this paper we introduce, for such algebras, the notions of ideal, tensor product, unitization, inverses, weak inverses, quasi-inverses, weak quasi-inverses and the spectrum of an element and investigate them in detail. This leads to a considerable generalization of the corresponding notions and results in the theory of Banach spaces. (English) |
| Keyword:
|
totally convex algebra |
| Keyword:
|
Eilenberg-Moore algebra |
| Keyword:
|
Banach algebra |
| Keyword:
|
ideal |
| Keyword:
|
(weak) inverse |
| Keyword:
|
spectrum |
| MSC:
|
46H05 |
| MSC:
|
46H10 |
| MSC:
|
46H20 |
| MSC:
|
46H99 |
| MSC:
|
46K05 |
| MSC:
|
46K99 |
| MSC:
|
46M15 |
| MSC:
|
46M99 |
| idZBL:
|
Zbl 0763.46036 |
| idMR:
|
MR1189653 |
| . |
| Date available:
|
2009-01-08T17:55:08Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118490 |
| . |
| Reference:
|
[1] Bonsall F.F., Duncan J.: Complete normed algebras.Springer, Erg. Math., Berlin-Heidelberg-New York, 1973. Zbl 0271.46039, MR 0423029 |
| Reference:
|
[2] Bourbaki N.: Eléments de mathématiques.Algèbre, chap. III, Hermann, Paris, 1970. Zbl 0455.18010, MR 0274237 |
| Reference:
|
[3] Cohn P.M.: Universal algebra.Harper & Row, New York-Evanston-London, 1965. Zbl 0461.08001, MR 0175948 |
| Reference:
|
[4] Pelletier J.W., Rosický J.: Generating the monadic theory of C$^\ast $-algebras and related categories.Categorical topology and its relation to analysis, algebra and combinatorics, Conf. Proc. Prague 1988, World Scientif. Publ. Singapore, New Jersey, London, Hongkong (1989), 163-180. MR 1047899 |
| Reference:
|
[5] Pierce R.S.: Introduction to the theory of abstract algebras.Holt, Rinehart and Winston, New York, 1965. MR 0227070 |
| Reference:
|
[6] Pumplün D., Röhrl H.: Banach spaces and totally convex spaces I.Comm. Alg. 12 (1984), 953-1019. MR 0735910 |
| Reference:
|
[7] Pumplün D., Röhrl H.: Banach spaces and totally convex spaces II.Comm. Alg. 13 (1985), 1047-1113. MR 0780637 |
| Reference:
|
[8] Pumplün D., Röhrl H.: Separated totally convex spaces.man. math. 50 (1985), 145-183. MR 0784142 |
| Reference:
|
[9] Pumplün D., Röhrl H.: The coproduct of totally convex spaces.Beitr. Alg. u. Geom. 24 (1987), 249-278. MR 0888218 |
| Reference:
|
[10] Pumplün D., Röhrl H.: Congruence relations on totally convex spaces.Comm. Alg. 18 (1990), 1469-1496. MR 1059742 |
| Reference:
|
[11] Pumplün D.: Regularly ordered Banach spaces and positively convex spaces.Results Math. 7 (1984), 85-112. MR 0758773 |
| Reference:
|
[12] Pumplün D.: The Hahn-Banach Theorem for totally convex spaces.Dem. Math. XVIII (1985), 567-588. MR 0819335 |
| Reference:
|
[13] Pumplün D.: Eilenberg-Moore algebras revisited.Seminarberichte, FB Mathematik u. Inf., Fernuniversität, 29 (1988), 97-144. |
| Reference:
|
[14] Rickart Ch.E.: General theory of Banach algebras.R.E. Krieger Publ. Co. Huntington, N.Y., 1974. Zbl 0095.09702 |
| Reference:
|
[15] Tholen W.: Relative Bildverzerlegungen und algebraische Kategorien.Ph.D. thesis, U. Münster, 1974. |
| . |
