Quasi-Banach Function Spaces
Quasi-Banach spaces are an important class of metrizable topological vector spaces (often, not locally convex), , , , , , ; for quasi-Banach lattices we refer to [82, pp. 1116-1119] and the references therein. In the past 20 years or so, the subclass of quasi-Banach function spaces has become relevant to various areas of analysis and operator theory; see, for example, , , , , , , , ,  and the references therein. Of particular importance is the notion of the p-th power X[p], 0 ≺ p ≺ ∞, of a given quasi-Banach function space X. This associated family of quasi-Banach function spaces X[ p ], which is intimately connected to the base space X, is produced via a procedure akin to that which produces the Lebesgue L p -spaces from L 1 (or more generally, produces the p-convexification of Banach lattices (of functions), , [99, pp. 53-54], ).
KeywordsBanach Lattice Lattice Norm Continuous Linear Operator Order Ideal Concavity Property
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