Abstract
Let X be a Banach space and denote by M(X) the Banach space of all X-valued measures, defined on the σ-algebra of Borel subsets of [0, 1], and equipped with the semivariation norm. Denote by M0(X) the (closed) subspace of M(X) consisting of the measures with relatively compact range. The aim of this paper is to prove that M0(X) is complemented in M(X) if and only if M0(X)=M(X).
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Rodríguez-Piazza, L. (2009). When is the Space of Compact Range Measures Complemented in the Space of All Vector-valued Measures?. In: Curbera, G.P., Mockenhaupt, G., Ricker, W.J. (eds) Vector Measures, Integration and Related Topics. Operator Theory: Advances and Applications, vol 201. Birkhäuser Basel. https://doi.org/10.1007/978-3-0346-0211-2_32
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DOI: https://doi.org/10.1007/978-3-0346-0211-2_32
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