| Title:
|
Pervasive algebras on planar compacts (English) |
| Author:
|
Čerych, Jan |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
40 |
| Issue:
|
3 |
| Year:
|
1999 |
| Pages:
|
491-494 |
| . |
| Category:
|
math |
| . |
| Summary:
|
We characterize compact sets $X$ in the Riemann sphere $\Bbb S$ not separating $\Bbb S$ for which the algebra $A(X)$ of all functions continuous on $\Bbb S$ and holomorphic on $\Bbb S\smallsetminus X$, restricted to the set $X$, is pervasive on $X$. (English) |
| Keyword:
|
compact Hausdorff space $X$ |
| Keyword:
|
the sup-norm algebra $C(X)$ of all complex-valued continuous functions on $X$ |
| Keyword:
|
its closed subalgebras (called function algebras) |
| Keyword:
|
pervasive algebras; the algebra $A(X)$ of all functions continuous on $\Bbb S$ and holomorphic on $\Bbb S\smallsetminus X$ |
| MSC:
|
30E10 |
| MSC:
|
46J10 |
| idZBL:
|
Zbl 1010.46051 |
| idMR:
|
MR1732486 |
| . |
| Date available:
|
2009-01-08T18:54:30Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119105 |
| . |
| Reference:
|
[1] Hoffman K., Singer I.M.: Maximal algebras of continuous functions.Acta Math. 103 (1960), 217-241. Zbl 0195.13903, MR 0117540 |
| Reference:
|
[2] Gamelin T.W.: Uniform Algebras.Prentice Hall, Inc., Englewood Cliffs, N.J., 1969. Zbl 1118.47014, MR 0410387 |
| Reference:
|
[3] Fuka J.: A remark to maximality of several function algebras (in Russian).Čas. Pěst. Mat. 93 (1968), 346-348. MR 0251539 |
| Reference:
|
[4] Saks S., Zygmund A.: Analytic Functions.Polskie Towarzystwo Matematyczne, Warszawa, 1952. Zbl 0136.37301, MR 0055432 |
| Reference:
|
[5] Urysohn P.S.: Sur une fonction analytique partout continue.Fund. Math. 4 (1922), 144-150. |
| Reference:
|
[6] McKissick R.: A nontrivial normal sup norm algebra.Bull. Amer. Math. Soc. 69 (1963), 391-395. Zbl 0113.31502, MR 0146646 |
| . |
