[CITATION][C] Inequalities for dominated mappings
SA Malyugin�- Siberian Mathematical Journal, 1996 - Springer
SA Malyugin
Siberian Mathematical Journal, 1996•SpringerOperator analogs of Bochner's theorem on the Fourier transform of a positive definite
mapping on a locally compact Abelian group were considered earlier in [1-3]. In [4], a vector
version was obtained of Bochner's theorem for dominated mappings acting from a locally
compact Abelian group into an order complete lattice-normed space. During the proof, new
inequalities were found for functions on a group. Apparently, these inequalities may be of
interest in their own right, and the present article is devoted to studying them. Let F be a�…
mapping on a locally compact Abelian group were considered earlier in [1-3]. In [4], a vector
version was obtained of Bochner's theorem for dominated mappings acting from a locally
compact Abelian group into an order complete lattice-normed space. During the proof, new
inequalities were found for functions on a group. Apparently, these inequalities may be of
interest in their own right, and the present article is devoted to studying them. Let F be a�…
Operator analogs of Bochner's theorem on the Fourier transform of a positive definite mapping on a locally compact Abelian group were considered earlier in [1-3]. In [4], a vector version was obtained of Bochner's theorem for dominated mappings acting from a locally compact Abelian group into an order complete lattice-normed space. During the proof, new inequalities were found for functions on a group. Apparently, these inequalities may be of interest in their own right, and the present article is devoted to studying them.
Let F be a universally complete K-space with a fixed order unity 1. Define order multiplication in F so that 1 become a ring unity (see [5]). Denote the complexification of F by Ft. Let Y be a vector space over C. A vector norm (F-norm) is a mapping I']: Y~ F satisfying the axioms Izl= 0** x= 0, Ix+ yl _< lxl+ lyl, and Ic l= Icll l (x, ye Y and c EC). The triple (Y, Il, F) is referred to as a complex lattice-normed space (see [6]). We assume-PC to be lattice-normed with
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