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New classes of Banach spaces which are \(M\)-ideals in their biduals. (English) Zbl 0787.46020

A subspace \(X\) of a Banach space \(Y\) is called an \(M\)-ideal if there is a projection \(P\) on \(Y'\) whose kernel is the annihilator of \(X\) such that \(\| y'\|= \| Py'\|+ \| y'- Py'\|\) for all \(y'\in Y'\). The author gives new examples of Banach spaces which are \(M\)-ideals in their biduals among sequence spaces, spaces of measurable functions, spaces of analytic functions, and operator spaces. Several known results are extended by this means. Some consequences are mentioned, for example, there are non-isometric \(M\)-embedded spaces with Banach-Mazur distance 1.

MSC:

46B20 Geometry and structure of normed linear spaces
46B10 Duality and reflexivity in normed linear and Banach spaces
46B25 Classical Banach spaces in the general theory
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