A real seminorm with square property is submultiplicative
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A Seminorm with Square Property on a Complex Associative Algebra Is Submultiplicative
The result stated in the title is proved as a consequence of an appropriate generalization replacing the square property of a seminorm with a similar weaker property which implies an equivalence to the supnorm of all continuous functions on a compact Hausdorff space also. Theorem. Let p be a seminorm with the square property on a complex (associative) algebra A. Then the following hold for all ...
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