کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
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4616093 | 1339338 | 2014 | 19 صفحه PDF | دانلود رایگان |
The paper is concerned with a special class of positive linear operators acting on the space C(K)C(K) of all continuous functions defined on a convex compact subset K of RdRd, d⩾1d⩾1, having non-empty interior. Actually, this class consists of all positive linear operators T on C(K)C(K) which leave invariant the polynomials of degree at most 1 and which, in addition, map polynomials into polynomials of the same degree. Among other things, we discuss the existence of such operators in the special case where K is strictly convex by also characterizing them within the class of positive projections. In particular we show that such operators exist if and only if ∂K is an ellipsoid. Furthermore, a characterization of balls of RdRd in terms of a special class of them is furnished. Additional results and illustrative examples are presented as well.
Journal: Journal of Mathematical Analysis and Applications - Volume 415, Issue 1, 1 July 2014, Pages 477–495