September 2022
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11 Reads
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1 Citation
Journal of Mathematical Analysis and Applications
The paper investigates free and projective L-spaces, where L is a given normed space. These spaces form a far-reaching generalization of known p-multinormed spaces; in particular, if L=Lp(X), the L-spaces can be considered as p-multinormed spaces, based on arbitrary σ-finite measure spaces X (for “canonical” p-multinormed spaces, X=N with the counting measure). We first describe a “naturally appearing” functor, based on paving L with contractively complemented finite dimensional subspaces. This finite dimensionality is essential; it permits us to describe a free L-space for this functor. As a corollary, we obtain a wide variety of projective L-spaces. For “nice” spaces L (such as the space of simple p-integrable functions on a measure space), we obtain a full characterization of projective L-spaces; as a particular case, we recover a description of projective p-multinormed spaces.