Katsaras, A. K. and Benekas, V.:
On weighted inductive limits of non-Archimedean spaces of continuous functions
Bollettino dell'Unione Matematica Italiana Serie 8 3-B (2000), fasc. n.3, p. 757-774, Unione Matematica Italiana (English)
pdf (306 Kb), djvu (249 Kb). | MR1801619 | Zbl 0972.46045
Sunto
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.
Referenze Bibliografiche
[1]
F. BASTIN,
On bornological $C\overline{V}(X)$ spaces,
Arch. Math.,
53 (
1989), 394-398. |
MR 1016004 |
Zbl 0693.46022[2]
F. BASTIN,
Weighted spaces of continuous functions,
Bull. Soc. Roy. Sc. Liège,
1 (
1990), 1-81. |
MR 1039680 |
Zbl 0705.46010[3]
F. BASTIN-
B. ERNST,
A criterion for $CV(X)$ to be quasinormable,
Results in Math.,
14 (
1988), 223-230. |
MR 964041 |
Zbl 0705.46011[4]
K. D. BIERSTEDT,
The approximation property for weighted function spaces,
Bonner Math. Schriften,
81 (
1975), 3-25. |
MR 493282 |
Zbl 0333.46023[5]
K. D. BIERSTEDT,
Tensor products of weighted spaces,
Bonner Math. Schriften,
81 (
1975), 26-58. |
MR 493283 |
Zbl 0333.46024[6]
K. D. BIERSTEDT-
J. BONET,
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]
K. D. BIERSTEDT-
J. BONET,
Dual density conditions in (DF)-spaces I,
Results in Math.,
14 (
1988), 242-274. |
MR 964043 |
Zbl 0688.46002[8]
K. D. BIERSTEDT-
J. BONET,
Dual density conditions in (DF)-spaces,
Bull. Soc. Roy. Sc. Liège,
57 (
1988), 567-589. |
MR 986374 |
Zbl 0688.46003[9]
K. D. BIERSTEDT-
J. BONET,
Some results on $VC(X)$, pp. 181-194 in: T. Terzioglu (Ed.),
Advances in the theory of Fréchet spaces,
Kluwer Academic Publishers,
1989. |
MR 1083564 |
Zbl 0716.46026[10]
K. D. BIERSTEDT-
J. BONET,
Completeness of the (LB)-space $VC(X)$,
Arch. Math. (Basel),
56 (
1991), 281-288. |
MR 1091882 |
Zbl 0688.46004[11]
K. D. BIERSTEDT-
R. MEISE,
Distinguished echelon spaces and the projective description of weighted inductive limits of type $V_{d}C(X)$, 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]
K. D. BIERSTEDT-
R. MEISE-
W. H. SUMMERS,
A projective description of weighted inductive limits,
Trans. Amer. Math. Soc.,
272 (
1982), 107-160. |
MR 656483 |
Zbl 0599.46026[13]
K. D. BIERSTEDT-
R. MEISE-
W. H. SUMMERS,
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]
J. BONET,
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]
J. BONET,
On weighted inductive limits of spaces of continuous functions,
Math. Z.,
192 (
1986), 9-20. |
MR 835386 |
Zbl 0575.46025[16]
J. P. Q. CARNEIRO,
Non-Archimedean weighted approximation (in Portuguese),
An. Acad. Bras. Ci.,
50 (1) (
1978), 1-34. |
MR 473806 |
Zbl 0399.41033[17]
J. P. Q. CARNEIRO,
Non-Archimedean weighted approximation, pp. 121-131 in:
Approximation Theory and Functional Analysis (J. B. Prolla, editor),
North-Holland Publ. Co. (Amsterdam),
1979. |
MR 553418 |
Zbl 0432.41021[18]
N. DE GRANDE-DE KIMPE-
J. KĄKOL-
C. PEREZ-GARCIA-
W. H. SCHIKHOF,
$p$-adic locally convex inductive limits, pp. 159-222 in:
$p$p-adic Functional Analysis,
Marcel Dekker, Inc.,
Lecture Notes in Pure and Applied Mathematics,
192,
1997. |
MR 1459211 |
Zbl 0889.46063[19]
B. ERNST,
On the uniqueness of weighted (DF)-topologies,
Bull. Soc. Roy. Sc. de Liège,
5-6 (
1987), 451-461. |
MR 929910 |
Zbl 0645.46028[20]
B. ERNST-
P. SCHETTLER,
On weighted spaces with a fundamental sequence of bounded sets,
Arch. Math.,
47 (
1986), 552-559. |
MR 871295 |
Zbl 0612.46026[21]
A. K. KATSARAS-
A. BELOYIANNIS,
Non-Archimedean weighted spaces of continuous functions,
Rendiconti di Mat. Serie VII, vol.
16 (
1996), 545-562. |
MR 1451076 |
Zbl 0911.46049[22]
A. K. KATSARAS-
A. BELOYIANNIS,
On non-Archimedean weighted spaces of continuous functions, pp. 237-252 in:
$p$p-adic Functional Analysis,
Lecture Notes in Pure and Applied Mathematics 192,
Marcel Dekker,
1997. |
MR 1459213 |
Zbl 0947.46057[23]
A. K. KATSARAS-
A. BELOYIANNIS,
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]
L. NACHBIN,
Elements of Approximation Theory,
Van Nostrand Math. Studies,
14,
1967. |
MR 217483 |
Zbl 0173.41403[25]
J. B. PROLLA,
Weighted spaces of vector-valued continuous functions,
Ann. Mat. Pura Appl. (4)
89 (
1971), 145-158. |
MR 308771 |
Zbl 0224.46024[26]
W. H. SCHIKHOF,
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[27]
A. C. M. VAN ROOIJ,
Non-Archimedean Functional Analysis, New York and Basel,
Marcel Dekker, Inc.,
1978. |
MR 512894 |
Zbl 0396.46061