Weakly unconditionally convergent series in M-ideals.
Copyright policy )Weakly unconditionally convergent series in M-ideals.
The main result of this article is a structure theorem on separable complex Banach spaces E such that K(E) is an M-ideal in L(E). It is shown that if such a space has the approximation property, then it is isomorphic to an complemented subspace of a space with a shrinking unconditional finite dimensional decomposition. The proof blends topological techniques with Banach algebra methods. The assumption that E is a complex space was later shown to be unnecessary in an article of \textit{D. Li} and the first-named author [Ann. Mat. Fourier 39, No.2, 361- 372 (1989)].
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Summability and bases; functional analytic aspects of frames in Banach and Hilbert spaces, Banach algebra methods, structure theorem on separable complex Banach spaces, Article, 510.mathematics, Geometry and structure of normed linear spaces, approximation property, Ideals and subalgebras, complemented subspace of a space with a shrinking unconditional finite dimensional decomposition, M-ideal, Riesz operators; eigenvalue distributions; approximation numbers, \(s\)-numbers, Kolmogorov numbers, entropy numbers, etc. of operators
Summability and bases; functional analytic aspects of frames in Banach and Hilbert spaces, Banach algebra methods, structure theorem on separable complex Banach spaces, Article, 510.mathematics, Geometry and structure of normed linear spaces, approximation property, Ideals and subalgebras, complemented subspace of a space with a shrinking unconditional finite dimensional decomposition, M-ideal, Riesz operators; eigenvalue distributions; approximation numbers, \(s\)-numbers, Kolmogorov numbers, entropy numbers, etc. of operators
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