For analytic symbols continuous on the closed disk, the wem/essential norm of the integrated multiplication operator equals the integral of the wem-values iff all symbols share one boundary peak point and a common argument.
Kalton and Dirk Werner,Property(M),M-ideals, and almost isometric structure of Banach spaces, J
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Weak null maximum and integration of families of multiplication operators
For analytic symbols continuous on the closed disk, the wem/essential norm of the integrated multiplication operator equals the integral of the wem-values iff all symbols share one boundary peak point and a common argument.