UNCONDITIONAL CONVERGENCE IN THE STRONG OPERATOR TOPOLOGY AND l∞
Glasgow mathematical journal, Tome 53 (2011) no. 3, pp. 583-598
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In this paper we study non-complemented spaces of operators and the embeddability of l∞ in the spaces of operators L(X, Y), K(X, Y) and Kw*(X*, Y). Results of Bator and Lewis [2, 3] (Bull. Pol. Acad. Sci. Math.50(4) (2002), 413–416; Bull. Pol. Acad. Sci. Math.549(1) (2006), 63–73), Emmanuele [8–10] (J. Funct. Anal.99 (1991), 125–130; Math. Proc. Camb. Phil. Soc.111 (1992), 331–335; Atti. Sem. Mat. Fis. Univ. Modena42(1) (1994), 123–133), Feder [11] (Canad. Math. Bull.25 (1982), 78–81) and Kalton [16] (Math. Ann.208 (1974), 267–278), are generalised. A vector measure result is used to study the complementation of the spaces W(X, Y) and K(X, Y) in the space L(X, Y), as well as the complementation of K(X, Y) in W(X, Y). A fundamental result of Drewnowski [7] (Math. Proc. Camb. Phil. Soc. 108 (1990), 523–526) is used to establish a result for operator-valued measures, from which we obtain as corollaries the Vitali–Hahn–Saks–Nikodym theorem, the Nikodym Boundedness theorem and a Banach space version of the Phillips Lemma.
GHENCIU, IOANA; LEWIS, PAUL. UNCONDITIONAL CONVERGENCE IN THE STRONG OPERATOR TOPOLOGY AND l∞. Glasgow mathematical journal, Tome 53 (2011) no. 3, pp. 583-598. doi: 10.1017/S0017089511000152
@article{10_1017_S0017089511000152,
author = {GHENCIU, IOANA and LEWIS, PAUL},
title = {UNCONDITIONAL {CONVERGENCE} {IN} {THE} {STRONG} {OPERATOR} {TOPOLOGY} {AND} l\ensuremath{\infty}},
journal = {Glasgow mathematical journal},
pages = {583--598},
year = {2011},
volume = {53},
number = {3},
doi = {10.1017/S0017089511000152},
url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089511000152/}
}
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