STRONGLY BOUNDED REPRESENTING MEASURES AND CONVERGENCE THEOREMS
Glasgow mathematical journal, Tome 52 (2010) no. 3, pp. 435-445

Voir la notice de l'article provenant de la source Cambridge University Press

Let K be a compact Hausdorff space, X a Banach space and C(K, X) the Banach space of all continuous functions f: K → X endowed with the supremum norm. In this paper we study weakly precompact operators defined on C(K, X).
DOI : 10.1017/S0017089510000133
Mots-clés : Primary 46 E40, 46 G10, Secondary 46B20
GHENCIU, IOANA; LEWIS, PAUL. STRONGLY BOUNDED REPRESENTING MEASURES AND CONVERGENCE THEOREMS. Glasgow mathematical journal, Tome 52 (2010) no. 3, pp. 435-445. doi: 10.1017/S0017089510000133
@article{10_1017_S0017089510000133,
     author = {GHENCIU, IOANA and LEWIS, PAUL},
     title = {STRONGLY {BOUNDED} {REPRESENTING} {MEASURES} {AND} {CONVERGENCE} {THEOREMS}},
     journal = {Glasgow mathematical journal},
     pages = {435--445},
     year = {2010},
     volume = {52},
     number = {3},
     doi = {10.1017/S0017089510000133},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089510000133/}
}
TY  - JOUR
AU  - GHENCIU, IOANA
AU  - LEWIS, PAUL
TI  - STRONGLY BOUNDED REPRESENTING MEASURES AND CONVERGENCE THEOREMS
JO  - Glasgow mathematical journal
PY  - 2010
SP  - 435
EP  - 445
VL  - 52
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.1017/S0017089510000133/
DO  - 10.1017/S0017089510000133
ID  - 10_1017_S0017089510000133
ER  - 
%0 Journal Article
%A GHENCIU, IOANA
%A LEWIS, PAUL
%T STRONGLY BOUNDED REPRESENTING MEASURES AND CONVERGENCE THEOREMS
%J Glasgow mathematical journal
%D 2010
%P 435-445
%V 52
%N 3
%U http://geodesic.mathdoc.fr/articles/10.1017/S0017089510000133/
%R 10.1017/S0017089510000133
%F 10_1017_S0017089510000133

[1] 1.Abbott, C., Weakly precompact and GSP operators on continuous function spaces, Bull. Polish Acad. Sci. Math. 37 (1989), 467–476. Google Scholar

[2] 2.Abott, C., Bator, E. and Lewis, P., Strictly singular and cosingular operators on spaces of continuous functions, Math. Proc. Camb. Phil. Soc. 110 (1991), 505–521. Google Scholar | DOI

[3] 3.Abott, C., Bator, E., Bilyeu, R. and Lewis, P., Weak precompactness, strong boundedness, and weak complete continuity, Math. Proc. Camb. Phil. Soc. 108 (1990), 325–335. Google Scholar | DOI

[4] 4.Bartle, R. G., A general bilinear vector integral, Studia Math. 15 (1956), 337–352. Google Scholar | DOI

[5] 5.Bator, E., Lewis, P. and Ochoa, J., Evaluation maps, restriction maps, and compactness, Colloq. Math. 78 (1998), 1–17. Google Scholar | DOI

[6] 6.Bator, E. and Lewis, P., Operators having weakly precompact adjoints, Math. Nachr. 157 (1992), 99–103. Google Scholar | DOI

[7] 7.Batt, J. and Berg, E. J., Linear bounded transformations on the space of continuous functions, J. Funct. Anal. 4 (1969), 215–239. Google Scholar | DOI

[8] 8.Bello, C. F., On weakly compact and unconditionally converging operators in spaces of vector-valued functions, Revista Real Acad. Madrid 81 (1987), 693–706. Google Scholar

[9] 9.Bessaga, C., Pelczynski, A., On bases and unconditional convergence of series in Banach spaces, Studia Math. 17 (1958), 151–164. Google Scholar | DOI

[10] 10.Bombal, F., On (V*) sets and Pelczynski's property (V*), Glasgow Math. J. 32 (1990), 109–120. Google Scholar | DOI

[11] 11.Bombal, F. and Porras, B., Strictly singular and strictly cosingular operators on C(K, E), Math. Nachr. 143 (1989), 355–364. Google Scholar | DOI

[12] 12.Bourgain, J., An averaging result for ℓ sequences and applications to weakly conditionally compact sets in L 1, Israel J. Math. 32 (1979), 289–298. Google Scholar | DOI

[13] 13.Bombal, F., Cembranos, P., Characterizations of some classes of operators on spaces of vector-valued continuous functions, Math. Proc. Camb. Phil. Soc. 97 (1985), 137–146. Google Scholar | DOI

[14] 14.Brooks, J. K. and Lewis, P., Linear Operators and vector measures, Trans. Amer. Math. Soc. 192 (1974), 139–162. Google Scholar | DOI

[15] 15.Cembranos, P., Kalton, N., Saab, E. and Saab, P., Pelczyinski's Property (V) on C(Ω, E) spaces, Math. Ann. 271 (1985), 91–97. Google Scholar | DOI

[16] 16.Diestel, J., Sequences and series in Banach spaces, Grad. texts in math., no. 92 (Springer-Verlag, Berlin, 1984). Google Scholar | DOI

[17] 17.Diestel, J. and Uhl, J. J. Jr., Vector measures, math. surveys 15 (American Mathematical Society, Rhode Island, 1977. Google Scholar | DOI

[18] 18.Dinculeanu, N., Vector measures (Pergamon Press, Oxford, UK, 1967). Google Scholar | DOI

[19] 19.Dobrakov, I., On representation of linear operators on C (T, X), Czechoslovak. Math. J. 21 (1971), 13–30. Google Scholar

[20] 20.Dunford, N. and Schwartz, J.T., Linear operators. Part I: General theory (Wiley-Interscience, New Jersey, 1958). Google Scholar

[21] 21.Emmanuele, G., Another proof of a result of N. J. Kalton, E. Saab and P. Saab on the Dieudonné property in C(K, E), Glasgow Math. J. 31 (1989), 137–140. Google Scholar | DOI

[22] 22.Emmanuele, G., On the Banach spaces with property (V*) of Pelczyinksi. II. Ann. Mat. Pura Appl. 160 (1991), 163–170. Google Scholar | DOI

[23] 23.Gamlen, J. L. B., On a theorem of Pelczyinski, Proc. Amer. Math. Soc. 44 (1974), 283–285. Google Scholar

[24] 24.Ghenciu, I. and Lewis, P., Almost weakly compact operators, Bull. Polish. Acad. Sci. Math. 54 (2006), 237–256. Google Scholar | DOI

[25] 25.Grothendieck, A., Sur les applications linéaires faiblement compactes d'espaces du type C(K), Canad. J. Math. 5 (1953), 129–173. Google Scholar | DOI

[26] 26.Kalton, N., Saab, E. and Saab, P., On the Dieudonné property for C(Ω, E), Proc. Amer. Math. Soc. 96 (1986), 50–52. Google Scholar

[27] 27.Pelczyinski, A., Banach spaces on which every unconditionally converging operator is weakly compact, Bull. Acad. Polon. Sci. Math. Astronom. Phys. 10 (1962), 641–648. Google Scholar

[28] 28.Swartz, C., Unconditionally converging and Dunford–Pettis operators on C (S), Studia Math. 57 (1976), 85–90. Google Scholar | DOI

[29] 29.Saab, E. and Saab, P., A stability property of Banach spaces not containing a complemented copy of ℓ, Proc. Amer. Math. Soc. 84 (1982), 44–46. Google Scholar

[30] 30.Talagrand, M., Weak Cauchy sequences in L 1(E), Amer. J. Math. 106 (1984), 703–724. Google Scholar | DOI

[31] 31.Talagrand, M., La proprieté de Dunford-Pettis dans C(K, E) et L 1(E), Israel J. Math. 44 (1983), 317–321. Google Scholar | DOI

[32] 32.Ülger, A., Continuous linear operators on C(K, X) and pointwise weakly precompact subsets of C(K, X), Math. Proc. Camb. Phil. Soc. 111 (1992), 143–150. Google Scholar

Cité par Sources :