Operator norms,multiplicativity factors,and C-numerical radii |
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Authors: | Moshe Goldberg EG Straus |
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Institution: | Department of Mathematics Technion—Israel Institute of Technology Haifa, Israel;Institute for the Interdisciplinary Applications of Algebra and Combinatorics University of California Santa Barbara, California 93106, USA;Department of Mathematics University of California Los Angeles, California 90024, USA |
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Abstract: | Let V be a normed vector space over C, let (V) denote the algebra of linear bounded operators on V, and let N be an arbitrary seminorm or norm on (V). In this paper we discuss multiplicativity factors for N, i.e., constants μ>0 for which Nμ≡μN is submultiplicative. We find that, while in the finite dimensional case nontrivial indefinite seminorms have no multiplicativity factors and norms do have multiplicativity factors, in the infinite dimensional case N may or may not have such factors. Our results are then applied in order to compute multiplicativity factors for certain generalizations of the classical numerical radius, called C-numerical radii. This is done with the help of a combinatorial inequality which seems to be of independent interest. |
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