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Quasi-Banach Function Spaces

Part of the Operator Theory: Advances and Applications book series (OT, volume 180)

Abstract

Quasi-Banach spaces are an important class of metrizable topological vector spaces (often, not locally convex), [70], [83], [87], [88], [105], [135]; 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, [29], [30], [32], [50], [59], [61], [87], [126], [152] 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), [9], [99, pp. 53-54], [157]).

Keywords

Banach Lattice Lattice Norm Continuous Linear Operator Order Ideal Concavity Property 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Birkhäuser Verlag AG 2008

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