Abstract
In this paper, we introduce the notion of the spherical p-quasinorms for operator tuples, and study some of their properties. We prove several inequalities and relations involving the different types of joint operator norms and spherical p-quasinorms, giving refinements of some fundamental inequalities, along the way. Among other things, we prove that ‖T‖Q,p=ωp(T), for any p>1 and any range-orthogonal normal tuple T. Finally, we also consider the asymptotic behaviour of p-quasinorms when p→0+ and use it to derive some bounds for the product of commuting normal operators.
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