| Title:
|
Cotype and complemented copies of $c_0$ in spaces of operators (English) |
| Author:
|
Bonet, J. |
| Author:
|
Domański, P. |
| Author:
|
Lindström, M. |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
46 |
| Issue:
|
2 |
| Year:
|
1996 |
| Pages:
|
271-289 |
| . |
| Category:
|
math |
| . |
| MSC:
|
46B28 |
| MSC:
|
47D15 |
| idZBL:
|
Zbl 0870.46016 |
| idMR:
|
MR1388616 |
| DOI:
|
10.21136/CMJ.1996.127290 |
| . |
| Date available:
|
2009-09-24T09:56:31Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127290 |
| . |
| Reference:
|
[A] S. I. Ansari: On Banach spaces $Y$ for which $B(C(\Omega ),Y)= K(C(\Omega ),Y)$.Pacific J. Math (to appear). Zbl 0831.47015, MR 1346253 |
| Reference:
|
[AD] R. Anantharaman, J. Diestel: Sequences in the range of a vector measure.Comment. Math. 30 (1991), 221–235. MR 1122692 |
| Reference:
|
[B] K. D. Bierstedt: An introduction to locally convex inductive limits.Functional Analysis and its Applications, World Sci., Singapore, 1988, pp. 35–133. Zbl 0786.46001, MR 0979516 |
| Reference:
|
[BDLR] J. Bonet, P. Domański, M. Lindström and M. S. Ramanujan: Operator spaces containing $c_0$ or $l^\infty $.Results Math (to appear). MR 1356892 |
| Reference:
|
[BL1] J. Bonet and M. Lindström: Spaces of operators between Fréchet spaces.Math. Proc. Cambridge Phil. Soc. 115 (1994), 133–144. MR 1253288, 10.1017/S0305004100071978 |
| Reference:
|
[BL2] J. Bonet and M. Lindström: Convergent sequences in duals of Fréchet spaces.Functional Analysis, K. D. Bierstedt, A. Pietsch, W. Ruess, D. Vogt (eds.), Proc. Essen Conf. 1991, Marcel Dekker, New York, 1993, pp. 391–404. MR 1241690 |
| Reference:
|
[Ct] J. M. F. Castillo: On Banach spaces X such that $L(L_p,X)=K(L_p, X)$.Preprint. |
| Reference:
|
[Ce] P. Cembranos: $C(K,E)$ contains a complemented copy of $c_0$.Proc. Amer. Math. Soc. 91 (1984), 556–558. MR 0746089 |
| Reference:
|
[CoRu] M. S. Collins, W. Ruess: Weak compactness in spaces of compact operators and of vector valued functions.Pac. J. Math. 106 (1982), 45–71. MR 0694671, 10.2140/pjm.1983.106.45 |
| Reference:
|
[Da] J. Dazord: Factoring operators through $c_0$.Math. Ann. 220 (1976), 105–122. Zbl 0304.47026, MR 0420318, 10.1007/BF01351695 |
| Reference:
|
[DF] A. Defant, K. Floret: Tensor Norms and Operator Ideals.North-Holland Math. Studies 176, North-Holland, Amsterdam, 1993. MR 1209438 |
| Reference:
|
[Dz] J. C. Díaz: Montel subspaces in the countable projective limits of $L^p(\mu )$-spaces.Canad. Math. Bull. 32 (1989), 169–176. MR 1006742, 10.4153/CMB-1989-025-4 |
| Reference:
|
[DzS] S. Díaz: Complemented copies of $c_0$ in $L^\infty (\mu ,E)$.Proc. Amer. Math. Soc. 120 (1994), 1167–1172. MR 1189744, 10.1090/S0002-9939-1994-1189744-1 |
| Reference:
|
[D1] J. Diestel: Sequences and Series in Banach Spaces.Springer, New York, 1984. MR 0737004 |
| Reference:
|
[DD1] P. Domański and L. Drewnowski: Uncomplementability of the spaces of norm continuous functions in some spaces of “weakly” continuous functions.Studia Math. 97 (1991), 245–251. MR 1100690, 10.4064/sm-97-3-245-251 |
| Reference:
|
[DD2] P. Domański and L. Drewnowski: Fréchet spaces of continuous vector-valued functions: Complementability in dual Fréchet spaces and injectivity.Studia Math. 102 (1992), 257–267. MR 1170555, 10.4064/sm-102-3-257-267 |
| Reference:
|
[DD3] P. Domański and L. Drewnowski: Complementability and injectivity of Fréchet spaces of continuous vector-valued functions.Functional Analysis, K. D. Bierstedt, A. Pietsch, W. Ruess, D. Vogt (eds.), Proc. Essen Conf. 1991, Marcel Dekker, New York, 1993, pp. 405–413. MR 1241691 |
| Reference:
|
[DD4] P. Domański and L. Drewnowski: Injectivity of spaces of bounded vector sequences and of spaces of operators.Preprint (1992). MR 1170555 |
| Reference:
|
[DL] P. Domański, M. Lindström: Grothendieck spaces and duals of injective tensor products.Preprint (1994). MR 1405494 |
| Reference:
|
[Dr1] L. Drewnowski: An extension of a theorem of Rosenthal on operators acting from $l^\infty (\Gamma )$.Studia Math. 62 (1976), 207–215. MR 0423116 |
| Reference:
|
[Dr2] L. Drewnowski: Copies of $l^\infty $ in an operator space.Math. Proc. Cambridge Phil. Soc. 108 (1990), 523–526. MR 1068453, 10.1017/S0305004100069401 |
| Reference:
|
[Dr3] L. Drewnowski: When does $ca(\Sigma ,X)$ contain a copy of $l_\infty $ or $c_0$?.Proc. Amer. Math. Soc. 109 (1990), 747–752. MR 1012927 |
| Reference:
|
[Dr4] L. Drewnowski: Another note on copies of $l_\infty $ and $c_0$ in $ca(\Sigma ,X)$ and the equality $ca(\Sigma ,X)=cca(\Sigma ,X)$.Preprint (1990). MR 1666614 |
| Reference:
|
[Dr5] L. Drewnowski: Private communication.. |
| Reference:
|
[DrE] L. Drewnowski, G. Emmanuele: The problem of complementability for some spaces of vector measures of bounded variation with values in Banach spaces containing copies of $c_0$.Studia Math. 104 (1993), 111–123. MR 1211812 |
| Reference:
|
[E1] G. Emmanuele: Remarks on the uncomplemented subspace $W(F,E)$.J. Funct. Analysis 99 (1991), 125–130. MR 1120917, 10.1016/0022-1236(91)90055-A |
| Reference:
|
[E2] G. Emmanuele: On complemented copies of $c_0$ in spaces of operators.Comment. Math. 32 (1992), 29–32. MR 1202755 |
| Reference:
|
[E3] G. Emmanuele: A remark on the containment of $c_0$ in spaces of compact operators.Math. Proc. Cambridge Phil. Soc. 111 (1992), 331–335. MR 1142753, 10.1017/S0305004100075435 |
| Reference:
|
[E4] G. Emmanuele: About the position of $K_{w^*}(E^{\prime },F)$ inside $L_{w^*}(E^{\prime },F)$.Atti Sem. Mat. Fis. Univ. Modena (to appear). MR 1282327 |
| Reference:
|
[E5] G. Emmanuele: About the uncomplementability of spaces of compact operators in larger spaces of operators.Preprint. |
| Reference:
|
[E6] G. Emmanuele: About the position of $K(X,Y)$ inside $DP(X,Y)$ and $W(X,Y)$.Preprint. |
| Reference:
|
[E7] G. Emmanuele: A note on Banach spaces containing complemented copies of $c_0$.Extracta Math. 3 (1988), 98–100. |
| Reference:
|
[E8] G. Emmanuele: On complemented copies of $c_0$ in spaces of operators II.Preprint. |
| Reference:
|
[E9] G. Emmanuele: Answer to a question by M. Feder about $K(X,Y)$.Rev. Mat. Complutense (Madrid) (to appear). Zbl 0813.46013, MR 1269756 |
| Reference:
|
[Fe1] M. Feder: On subspaces of spaces with an unconditional basis and spaces of operators.Illinois J. Math. 24 (1980), 196–205. Zbl 0411.46009, MR 0575060, 10.1215/ijm/1256047715 |
| Reference:
|
[Fe2] M. Feder: On the nonexistence of a projection onto the space of compact operators.Canad. Math. Bull. 25 (1982), 78–81. MR 0657655, 10.4153/CMB-1982-011-0 |
| Reference:
|
[Fl] K. Floret: Weakly Compact Sets.Lect. Notes Math., vol. 801, Springer, Berlin, 1980. Zbl 0437.46006, MR 0576235, 10.1007/BFb0091483 |
| Reference:
|
[Fr1] F. J. Freniche: Barreledness of the space of vector-valued and simple functions.Math. Ann. 267 (1984), 479–486. MR 0742894, 10.1007/BF01455966 |
| Reference:
|
[Fr2] F. J. Freniche: Grothendieck locally convex spaces of continuous vector-valued functions.Pacific J. Math. 120 (1985), 345–355. Zbl 0575.46036, MR 0810776, 10.2140/pjm.1985.120.345 |
| Reference:
|
[J] H. Jarchow: Locally Convex Spaces.Teubner, Stuttgart, 1981. Zbl 0466.46001, MR 0632257 |
| Reference:
|
[Jo1] K. John: On the uncomplemented subspace $K(X,Y)$.Czech. Math. J. 42 (1992), 167–173. Zbl 0776.46016, MR 1152178 |
| Reference:
|
[Jo2] K. John: On the space $K(P,P^*)$ of compact operators on Pisier space $P$.Note Mat. (Lecce) 12 (1992), 69–75. MR 1258564 |
| Reference:
|
[Ka1] N. J. Kalton: Spaces of compact operators.Math. Ann. 208 (1974), 267–278. Zbl 0266.47038, MR 0341154, 10.1007/BF01432152 |
| Reference:
|
[Ka2] N. J. Kalton: Exhaustive operators and vectors measures.Proc. Edinburgh Math. Soc. 19 (1975), 291–300. MR 0388099 |
| Reference:
|
[KRT] H. König, J. R. Retherford, N. Tomczak-Jaegermann: On the eigenvalues of $(p,2)$-summing operators and constants associated with normed spaces.J. Funct. Anal. 37 (1980), 88–126. MR 0576647, 10.1016/0022-1236(80)90029-4 |
| Reference:
|
[LT] J. Lindenstrauss, L. Tzafiri: Classical Banach Spaces.Lecture Notes in Math., vol. 338, Springer, Berlin, 1973. MR 0415253 |
| Reference:
|
[L] M. Lindström: A characterization of Schwartz spaces.Math. Z. 198 (1988), 423–430. MR 0946613, 10.1007/BF01184675 |
| Reference:
|
[LS] M. Lindström and T. Schlumprecht: A Josefson-Nissenzweig theorem for Fréchet spaces.Bull. London Math. Soc. 25 (1993), 55–58. MR 1190364, 10.1112/blms/25.1.55 |
| Reference:
|
[MR] C. W. McArthur, J. R. Rutherford: Some applications of an inequality in locally convex spaces.Trans. Amer. Math. Soc. 137 (1969), 115–123. MR 0239391, 10.1090/S0002-9947-1969-0239391-0 |
| Reference:
|
[Me] J. Mendoza: Copies of $l_\infty $ in $L^p(\mu , X)$.Proc. Amer. Math. Soc. 109 (1990), 125–127. MR 1012935 |
| Reference:
|
[OP] R. I. Ovsepian, A. Pełczyński: On the existence of a fundamental total and bounded biorthogonal sequence in every separable Banach space, and related constructions of uniformly bounded orthogonal systems in $L^2$.Studia Math. 54 (1975), 149–159. MR 0394137, 10.4064/sm-54-2-149-159 |
| Reference:
|
[PS] A. Pełczyński and Z. Semadeni: Spaces of continuous functions III.Studia Math 18 (1958), 211–222. MR 0107806 |
| Reference:
|
[PCB] P. Pérez Carreras and J. Bonet: Barrelled Locally Convex Spaces.North-Holland Mathematics Studies, vol. 131, Elsevier/North-Holland, Amsterdam, 1987. MR 0880207 |
| Reference:
|
[Ra] F. Räbiger: Beiträge zur Strukturtheorie der Grothendieckräume.Sitzungber. Heidelb. Akad. Wiss. Math.-Natur. Kl. Abh. 4 (1985). |
| Reference:
|
[Rh] K. Reiher: Weighted inductive and projective limits of normed Köthe function spaces.Results Math. 13 (1988), 147–161. Zbl 0636.46023, MR 0928147, 10.1007/BF03323402 |
| Reference:
|
[Ry] R. Ryan: Complemented copies of $c_0$ in injective tensor products and spaces of compact operators.Proc. Congreso de Analysis Funcional, El Escorial, Madrid, 1988, pp. 13–18. |
| Reference:
|
[Sa] F. Saab and P. Saab: On complemented copies of $c_0$ in injective tensor products.Contemporary Math. 52 (1986), 131–135. 10.1090/conm/052/840704 |
| Reference:
|
[S] Th. Schlumprecht: Limited sets in Banach spaces.Dissertation (1987), München. |
| Reference:
|
[T1] M. Talagrand: Cotype of operators from $C(K)$.Invent. Math. 107 (1992), 1–40. Zbl 0788.47022, MR 1135462, 10.1007/BF01231879 |
| Reference:
|
[T2] M. Talagrand: Cotype and $(q,1)$-summing norm in a Banach space.Invent. Math. 110 (1992), 545–556. Zbl 0814.46010, MR 1189490, 10.1007/BF01231344 |
| Reference:
|
[TJ] N. Tomczak-Jaegermann: The moduli of smoothness and convexity and the Rademacher average of trace class $S_p$.Studia Math. 50 (1974), 163–182. MR 0355667 |
| Reference:
|
[Wl] L. J. Weill: Unconditional and shrinking bases in locally convex spaces.Pacific J. Math. 29 (1969), 467–483. Zbl 0176.10802, MR 0246083, 10.2140/pjm.1969.29.467 |
| . |
