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Inversion of the oscillatory property of focusing operators
Yu. V. Pokornyi, S. V. Smitskikh Voronezh State University
Abstract:
Suppose that $E$ is a real Banach space with a cone $K$ and suppose that the homogeneous additive operator $A$ that is positive on $K$ is focusing, i.e., $AK\subset K_{u_0\rho}$ for certain $u_0\in K$ and $\rho\ge1$. Then, as is well known, the operator $A$ uniformly reduces the oscillation (osc) between the elements of $K$. In this paper we show that only the focusing operators have this property.
Received: 07.07.1972
Citation:
Yu. V. Pokornyi, S. V. Smitskikh, “Inversion of the oscillatory property of focusing operators”, Mat. Zametki, 20:5 (1976), 753–760; Math. Notes, 20:5 (1976), 980–984
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https://www.mathnet.ru/eng/mzm7902 https://www.mathnet.ru/eng/mzm/v20/i5/p753
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Abstract page: | 174 | Full-text PDF : | 83 | First page: | 1 |
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