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Register a new userCompletely strong superadditivity of generalized matrix functions
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We prove that generalized matrix functions satisfy a block-matrix strong superadditivity inequality over the cone of positive semidefinite matrices. Our result extends a recent result of Paksoy-Turkmen-Zhang (V. Paksoy, R. Turkmen, F. Zhang, Inequalities of generalized matrix functions via tensor products, Electron. J. Linear Algebra 27 (2014) 332-341.). As an application, we obtain a short proof of a classical inequality of Thompson (1961) on block matrix determinants.
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New classes of generalized Nevanlinna functions, which under multiplication with an arbitrary fixed symmetric rational function remain generalized Nevanlinna functions, are introduced. Characterizations for these classes of functions are established by connecting the canonical factorizations of the product function and the original generalized Nevanlinna function in a constructive manner. Also a detailed functional analytic treatment of these classes of functions is carried out by investigating the connection between the realizations of the product function and the original function. The operator theoretic treatment of these realizations is based on the notions of rigged spaces, boundary triplets, and associated Weyl functions.
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The properties of the compactness of interpolation sets of algebras of generalized analytic functions are investigated and convenient sufficient conditions for interpolation are given.
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