Si studiano alcune proprietà di un certo limite induttivo di spazi non-archimedei di funzioni continue. In particolare, si esamina la completezza di questo limite induttivo e si indaga il problema di quando lo spazio coincide con il proprio inviluppo proiettivo.
@article{BUMI_2000_8_3B_3_757_0, author = {A. K. Katsaras and V. Benekas}, title = {On weighted inductive limits of non-Archimedean spaces of continuous functions}, journal = {Bollettino dell'Unione Matematica Italiana}, volume = {3-A}, year = {2000}, pages = {757-774}, zbl = {0972.46045}, mrnumber = {1801619}, language = {en}, url = {http://dml.mathdoc.fr/item/BUMI_2000_8_3B_3_757_0} }
Katsaras, A. K.; Benekas, V. On weighted inductive limits of non-Archimedean spaces of continuous functions. Bollettino dell'Unione Matematica Italiana, Tome 3-A (2000) pp. 757-774. http://gdmltest.u-ga.fr/item/BUMI_2000_8_3B_3_757_0/
[1] On bornological spaces, Arch. Math., 53 (1989), 394-398. | MR 1016004 | Zbl 0693.46022
,[2] Weighted spaces of continuous functions, Bull. Soc. Roy. Sc. Liège, 1 (1990), 1-81. | MR 1039680 | Zbl 0705.46010
,[3] A criterion for to be quasinormable, Results in Math., 14 (1988), 223-230. | MR 964041 | Zbl 0705.46011
- ,[4] The approximation property for weighted function spaces, Bonner Math. Schriften, 81 (1975), 3-25. | MR 493282 | Zbl 0333.46023
,[5] Tensor products of weighted spaces, Bonner Math. Schriften, 81 (1975), 26-58. | MR 493283 | Zbl 0333.46024
,[6] Stefan Heinrich's density condition for Fréchet spaces and the characterization of the distinguished Köthe echelon spaces, Math. Nach., 135 (1988), 149-180. | MR 944226 | Zbl 0688.46001
- ,[7] Dual density conditions in (DF)-spaces I, Results in Math., 14 (1988), 242-274. | MR 964043 | Zbl 0688.46002
- ,[8] Dual density conditions in (DF)-spaces, Bull. Soc. Roy. Sc. Liège, 57 (1988), 567-589. | MR 986374 | Zbl 0688.46003
- ,[9] Some results on , pp. 181-194 in: (Ed.), Advances in the theory of Fréchet spaces, Kluwer Academic Publishers, 1989. | MR 1083564 | Zbl 0716.46026
- ,[10] Completeness of the (LB)-space , Arch. Math. (Basel), 56 (1991), 281-288. | MR 1091882 | Zbl 0688.46004
- ,[11] Distinguished echelon spaces and the projective description of weighted inductive limits of type , pp. 169-226 in: Aspects in Mathematics and its Applications, Elsevier Science Publ. B. V., North-Holland Math. Library, 1986. | MR 849552 | Zbl 0645.46027
- ,[12] A projective description of weighted inductive limits, Trans. Amer. Math. Soc., 272 (1982), 107-160. | MR 656483 | Zbl 0599.46026
- - ,[13] Köthe sets and Köthe sequence spaces, pp. 27-91 in: Functional Analysis, Holomorphy and Approximation Theory, North-Holland Math. Studies, 71, 1982. | MR 691159 | Zbl 0504.46007
- - ,[14] A projective description of weighted inductive limits of spaces of vector valued continuous functions, Collectanea Math., 34 (1983), 115-125. | MR 766993 | Zbl 0708.46037
,[15] On weighted inductive limits of spaces of continuous functions, Math. Z., 192 (1986), 9-20. | MR 835386 | Zbl 0575.46025
,[16] Non-Archimedean weighted approximation (in Portuguese), An. Acad. Bras. Ci., 50 (1) (1978), 1-34. | MR 473806 | Zbl 0399.41033
,[17] Non-Archimedean weighted approximation, pp. 121-131 in: Approximation Theory and Functional Analysis ( , editor), North-Holland Publ. Co. (Amsterdam), 1979. | MR 553418 | Zbl 0432.41021
,[18] -adic locally convex inductive limits, pp. 159-222 in: -adic Functional Analysis, Marcel Dekker, Inc., Lecture Notes in Pure and Applied Mathematics, 192, 1997. | MR 1459211 | Zbl 0889.46063
- - - ,[19] On the uniqueness of weighted (DF)-topologies, Bull. Soc. Roy. Sc. de Liège, 5-6 (1987), 451-461. | MR 929910 | Zbl 0645.46028
,[20] On weighted spaces with a fundamental sequence of bounded sets, Arch. Math., 47 (1986), 552-559. | MR 871295 | Zbl 0612.46026
- ,[21] Non-Archimedean weighted spaces of continuous functions, Rendiconti di Mat. Serie VII, vol. 16 (1996), 545-562. | MR 1451076 | Zbl 0911.46049
- ,[22] On non-Archimedean weighted spaces of continuous functions, pp. 237-252 in: -adic Functional Analysis, Lecture Notes in Pure and Applied Mathematics 192, Marcel Dekker, 1997. | MR 1459213 | Zbl 0947.46057
- ,[23] Tensor products of non-Archimedean weighted spaces of continuous functions, Georgian J. Math., Vol. 6, No 1 (1999), 33-44. | MR 1672990 | Zbl 0921.46085
- ,[24] Elements of Approximation Theory, Van Nostrand Math. Studies, 14, 1967. | MR 217483 | Zbl 0173.41403
,[25] Weighted spaces of vector-valued continuous functions, Ann. Mat. Pura Appl. (4) 89 (1971), 145-158. | MR 308771 | Zbl 0224.46024
,[26] Locally convex spaces over non-spherically complete valued fields I, II, Bul. Soc. Math. Belg., serie B XXXVIII (1986), 187-224. | MR 871313 | Zbl 0615.46071
, , Non-Archimedean Functional Analysis, New York and Basel, Marcel Dekker, Inc., 1978.