Factorization of p-th Power Factorable Operators through Lq-spaces
Maurey—Rosenthal factorization theory establishes a clear link between norm inequalities for operators, geometrical properties of Banach lattices, and factorizations through L q -spaces. This theory essentially has its roots in the work of Rosenthal, Krivine and Maurey (see , , , ). They developed these ideas in the late 1960s and during the 1970s for purposes related to the study of the structure of Banach lattices and operators. In the 1980s, the contributions of García Cuerva and Rubio de Francia provided powerful new tools for this theory in the context of harmonic analysis,  , . Currently, this factorization theory has become a keystone in several areas of functional analysis with varied applications, for instance, to interpolation theory of Banach spaces, operator ideal theory, , , the study of almost everywhere convergence of series in function spaces, [163, III.H] and to the factorization of inequalities, , , . Further contributions to the Maurey—Rosenthal theory have recently been developed in the context of the geometry of Banach lattices (see for instance , , ).
KeywordsBanach Space Integration Operator Measure Space Banach Lattice Vector Measure
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