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We prove new inequalities for the spectral radius, essential spectral radius,operator norm, measure of noncompactness and numerical radius of Hadamardweighted geometric means of positive kernel operators on Banach function andsequence spaces. Several inequalities appear to be new even in the finitedimensional case.

Hadamard weighted geometric mean inequalities for the spectral and  essential spectral radius of positive operators on Banach function and  sequence spaces