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This paper is devoted to the study of semi-LpB spaces, which coincide with the semi-LB spaces defined by Valdivia when p = 1. We give new results in localization and lifting. We study the relation between the class of semi-LpB spaces and the class of webbed spaces. Finally we obtain localization theorems without any convexity assumptions.
Let L be a normal Banach sequence space such that every element in L is the limit of its sections and let E = ind E be a separated inductive limit of the locally convex spaces. Then ind L(E) is a topological subspace of L(E).
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