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Deformations of positive linear operators of type B

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Abstract

The concept of the deformation of positive linear operators of type B is introduced, in particular, that of a linear deformation of operators. These concepts are applied to the solving of operator equations of type B. One solves completely the problems of the determination of all positive linear operators of type B for which the covariance of the operators is 1) a polynomial of degrees ≤3; 2) any power function; 3) an exponential function. In addition, one finds; two families of positive linear operators of type B for which the covariance is a polynomial of degree four.

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Authors and Affiliations

  1. Vinnitsa Polytechnic Institute, USSR

    Yu. I. Volkov

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  1. Yu. I. Volkov
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 7, pp. 888–900, July, 1990.

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Volkov, Y.I. Deformations of positive linear operators of type B. Ukr Math J 42, 785–796 (1990). https://doi.org/10.1007/BF01062080

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  • DOI: https://doi.org/10.1007/BF01062080

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