| Title:
|
A characterization of weighted $(LB)$-spaces of holomorphic functions having the dual density condition (English) |
| Author:
|
Wolf, Elke |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
58 |
| Issue:
|
3 |
| Year:
|
2008 |
| Pages:
|
741-749 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We characterize when weighted $(LB)$-spaces of holomorphic functions have the dual density condition, when the weights are radial and grow logarithmically. (English) |
| Keyword:
|
$(LB)$-spaces |
| Keyword:
|
weighted spaces of holomorphic functions |
| Keyword:
|
dual density condition |
| MSC:
|
46A04 |
| MSC:
|
46A13 |
| MSC:
|
46E10 |
| idZBL:
|
Zbl 1174.46014 |
| idMR:
|
MR2455935 |
| . |
| Date available:
|
2010-07-20T14:04:18Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140418 |
| . |
| Reference:
|
[1] Anderson, J. M., Duncan, J.: Duals of Banach spaces of entire functions.Glasgow Math. J. 32 (1990), 215-220. Zbl 0769.46011, MR 1058534, 10.1017/S0017089500009241 |
| Reference:
|
[2] Bastin, F.: Distinguishedness of weighted Fréchet spaces of continuous functions.Proc. Edinb. Math. Soc., II. Ser. 35 271-283. Zbl 0738.46006, MR 1169245, 10.1017/S0013091500005538 |
| Reference:
|
[3] Bierstedt, K. D., Bonet, J.: Stefan Heinrich's density condition and the characterization of the distinguished Köthe echelon spaces.Math. Nachr. 135 (1988), 149-180. MR 0944226, 10.1002/mana.19881350115 |
| Reference:
|
[4] Bierstedt, K. D., Bonet, J.: Dual density conditions in ${(DF)}$-spaces I.Results Math. 14 (1988), 242-274. Zbl 0688.46002, MR 0964043, 10.1007/BF03323229 |
| Reference:
|
[5] Bierstedt, K. D., Bonet, J.: Dual density conditions in ${(DF)}$-spaces {II}.Bull. Soc. Roy. Sci. Liège 57 (1988), 567-589. Zbl 0688.46003, MR 0986374 |
| Reference:
|
[6] Bierstedt, K. D., Bonet, J.: Biduality in {($LF$)}-spaces.RACSAM Rev. R. Acad. Cienc. Exactas Fis. Nat. Ser. A Math. 95 (2001), 171-180. Zbl 1034.46001, MR 1902422 |
| Reference:
|
[7] Bierstedt, K. D., Bonet, J., Galbis, A.: Weighted spaces of holomorphic functions on balanced domains.Michigan Math. J. 40 (1993), 271-297. Zbl 0803.46023, MR 1226832, 10.1307/mmj/1029004753 |
| Reference:
|
[8] Bierstedt, K. D., Bonet, J., Taskinen, J.: Associated weights and spaces of holomorphic functions.Studia Math. 127 (1998), 137-168. Zbl 0934.46027, MR 1488148 |
| Reference:
|
[9] Bierstedt, K. D., Meise, R., Summers, W. H.: A projective description of weighted inductive limits.Trans. Amer. Math. Soc. 272 (1982), 107-160. Zbl 0599.46026, MR 0656483, 10.1090/S0002-9947-1982-0656483-9 |
| Reference:
|
[10] Bonet, J., Engliš, M., Taskinen, J.: Weighted $L^{\infty}$-estimates for Bergman projections.Studia Math. 171 (2005), 67-92. MR 2182272, 10.4064/sm171-1-4 |
| Reference:
|
[11] Heinrich, S.: Ultrapowers of locally convex spaces and applications I.Math. Nachr. 118 (1984), 285-315. Zbl 0576.46002, MR 0773627, 10.1002/mana.19841180121 |
| Reference:
|
[12] Jarchow, H.: Locally Convex Spaces.Math. Leitfäden, B.G. Teubner, Stuttgart (1981). Zbl 0466.46001, MR 0632257 |
| Reference:
|
[13] Köthe, G.: Topological Vector Spaces I.Grundlehren der math. Wiss. 159, Springer-Verlag, New York-Berlin (1969). MR 0248498 |
| Reference:
|
[14] Meise, R., Vogt, D.: Introduction to Functional Analysis.Oxford Graduate Texts in Math. 2, The Clarendon Press, Oxford University Press, New York (1997). Zbl 0924.46002, MR 1483073 |
| Reference:
|
[15] Pérez-Carreras, P., Bonet, J.: Barrelled Locally Convex Spaces.North-Holland Math. Stud. 131, Amsterdam (1987). MR 0880207 |
| Reference:
|
[16] Peris, A.: Some results on Fréchet spaces with the density condition.Arch. Math. (Basel) 59 (1992), 286-293. Zbl 0732.46002, MR 1174407, 10.1007/BF01197327 |
| Reference:
|
[17] Wolf, E.: Weighted $(LB)$-spaces of holomorphic functions and the dual density conditions.RACSAM Rev. R. Acad. Cienc. Exactas Fis. Nat. Ser. A Mat. 99 (2005), 149-165. Zbl 1106.46017, MR 2216098 |
| Reference:
|
[18] Wolf, E.: The density condition and distinguishedness of weighted Fréchet spaces of holomorphic functions.J. Math. Anal. Appl. 327 (2007), 530-546. MR 2306820, 10.1016/j.jmaa.2006.06.071 |
| . |
