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Keywords:
factorization of linear operators; u-ideal; approximation properties; unconditional basis
factorization of linear operators; u-ideal; approximation properties; unconditional basis
Summary:
We suggest a method of renorming of spaces of operators which are suitably approximable by sequences of operators from a given class. Further we generalize J. Johnsons’s construction of ideals of compact operators in the space of bounded operators and observe e.g. that under our renormings compact operators are $u$-ideals in the: space of 2-absolutely summing operators or in the space of operators factorable through a Hilbert space.
References:
[E,J] G. Emmanuele, K. John: Some remarks on the position of the space ${\mathcal K}(X,Y)$ inside the space ${\mathcal W}(X,Y)$. New Zealand J. Math. 26(2) (1997), 183–189. MR 1601639
[F] J. H. Fourie: Projections on operator duals. Quaestiones Math. 21 (1998), 11–18. DOI 10.1080/16073606.1998.9632022 | MR 1658463 | Zbl 0938.47020
[G,K,S] G. Godefroy, N. J. Kalton, P. D. Saphar: Unconditional ideals in Banach spaces. Studia Math. 104 (1) (1993), 13–59. MR 1208038
[H,W,W] P. Harmand, D. Werner, W. Werner: M-ideals in Banach Spaces and Banach Algebras. Lecture Notes in Math., 1547, Springer, Berlin, 1993. MR 1238713
[J1] K. John: On the space ${\mathcal K}(P,P^\ast )$ of compact operators on Pisier space P. Note di Matematica 12 (1992), 69–75. MR 1258564
[J2] K. John: On a result of J. Johnson. Czechoslovak Math. Journal 45 (1995), 235–240. MR 1331461 | Zbl 0869.46011
[Jo] J. Johnson: Remarks on Banach spaces of compact operators. J. Funct. Analysis 32 (1979), 304–311. DOI 10.1016/0022-1236(79)90042-9 | MR 0538857 | Zbl 0412.47024
[Ka] N. J. Kalton: Spaces of compact operators. Math. Annalen 208 (1974), 267–278. DOI 10.1007/BF01432152 | MR 0341154 | Zbl 0266.47038
[Li] Å. Lima: Property $(wM^*)$ and the unconditional metric approximation property. Studia Math. 113 (3) (1995), 249–263. DOI 10.4064/sm-113-3-249-263 | MR 1330210 | Zbl 0826.46013
[LT,I] J. Lindenstrauss, L. Tzafriri: Classical Banach Spaces, Sequence Spaces. EMG 92 Springer Verlag (1977). MR 0500056
[LT,II] J. Lindenstrauss, L. Tzafriri: Classical Banach Spaces, Function Spaces. EMG 97 Springer Verlag (1979). MR 0540367
[Pie] A. Pietsch: Operator ideals. Berlin, Deutscher Verlag der Wissenschaften, 1978. MR 0519680 | Zbl 0405.47027
[Pi] J. Pisier: Counterexamples to a conjecture of Grothendieck. Acta Mat. 151 (1983), 180–208. MR 0723009 | Zbl 0542.46038
[Ru] W. Ruess: Duality and Geometry of spaces of compact operators. Functional Analysis: Surveys and Recent Results III, Math. Studies 90, North Holland, 1984, pp. 59–78. MR 0761373 | Zbl 0573.46007
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