Lebesgue Spaces of Matrix Functions
In this Chapter, we introduce the notations and define the spaces L p (G,M n ) ofmatrix L p functions on locally compact groups G as a setting for later developments. We recall some basic definitions and derive some results for convolution operators in the scalar case. We discuss differentiability of the norm in L p (G,M p which is needed later, and compute the Gateaux derivative of the norm when the matrix space M p is equipped with the Hilbert-Schmidt norm.
KeywordsBanach Space Matrix Function Compact Group Banach Algebra Lebesgue Space
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