MODIFIED BERNSTEIN-SCHNABL OPERATORS ON CONVEX COMPACT SUBSETS OF LOCALLY CONVEX SPACES AND THEIR LIMIT SEMIGROUPS

MIRELLA CAPPELLETTI MONTANO; SABRINA DIOMEDE

Title	MODIFIED BERNSTEIN-SCHNABL OPERATORS ON CONVEX COMPACT SUBSETS OF LOCALLY CONVEX SPACES AND THEIR LIMIT SEMIGROUPS
Publication Type	Journal Article
Year of Publication	2009
Authors	MONTANO, MIRELLACAPPELLETT, DIOMEDE, SABRINA
Volume	13
Issue	4
Start Page	609
Pagination	24
Date Published	2009
ISSN	1083-2564
AMS	41A36, 41A65, 47D03
Abstract	In this paper we introduce a sequence ${\ (M_n\ )\ _{n\geq\ n_0} }$ of positive linear operators as a modification of the Bernstein-Schnabl operators associated with a positive projection on ${ \ C(K) }$, where ${ \ K}$ is a convex compact subset of a locally convex space; moreover we study its main approximation and qualitative properties. Furthermore, we establish an asymptotic formula for those operators, and we prove that to the sequence ${\ (M_n\ )\ _{n\geq\ n_0} }$ there corresponds a uniquely determined ${ \ C_0 }$-semigroup (in some special case a Feller one) which is representable as a limit of suitable powers of the operator
URL	http://www.acadsol.eu/en/articles/13/4/12.pdf
Refereed Designation	Refereed
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