Complemented spaces of operators

Ghenciu, Ioana

doi:10.1090/S0002-9939-05-07932-3

Complemented spaces of operators
HTML articles powered by AMS MathViewer

by Ioana Ghenciu PDF

Proc. Amer. Math. Soc. 133 (2005), 2621-2623 Request permission

Abstract:

Classical results of Kalton are used to study the complementation of the space $W(X,Y)$ of weakly compact operators and the space $K(X,Y)$ of compact operators in the space $L(X,Y)$ of bounded linear operators from $X$ to $Y$.

References

Elizabeth Bator and Paul W. Lewis, Complemented spaces of operators, Bull. Polish Acad. Sci. Math. 50 (2002), no. 4, 413–416. MR 1948406
Joseph Diestel, Sequences and series in Banach spaces, Graduate Texts in Mathematics, vol. 92, Springer-Verlag, New York, 1984. MR 737004, DOI 10.1007/978-1-4612-5200-9
J. Diestel and J. J. Uhl Jr., Vector measures, Mathematical Surveys, No. 15, American Mathematical Society, Providence, R.I., 1977. With a foreword by B. J. Pettis. MR 0453964
G. Emmanuele, A remark on the containment of $c_0$ in spaces of compact operators, Math. Proc. Cambridge Philos. Soc. 111 (1992), no. 2, 331–335. MR 1142753, DOI 10.1017/S0305004100075435
G. Emmanuele, Remarks on the uncomplemented subspace $W(E,F)$, J. Funct. Anal. 99 (1991), no. 1, 125–130. MR 1120917, DOI 10.1016/0022-1236(91)90055-A
G. Emmanuele and K. John, Uncomplementability of spaces of compact operators in larger spaces of operators, Czechoslovak Math. J. 47(122) (1997), no. 1, 19–32. MR 1435603, DOI 10.1023/A:1022483919972
Moshe Feder, On the nonexistence of a projection onto the space of compact operators, Canad. Math. Bull. 25 (1982), no. 1, 78–81. MR 657655, DOI 10.4153/CMB-1982-011-0
Kamil John, On the uncomplemented subspace $K(X,Y)$, Czechoslovak Math. J. 42(117) (1992), no. 1, 167–173. MR 1152178
N. J. Kalton, Spaces of compact operators, Math. Ann. 208 (1974), 267–278. MR 341154, DOI 10.1007/BF01432152