Document Details Document Type : Article In Journal  Document Title : Some change of variable formulas in integral representation theory Some change of variable formulas in integral representation theory   Subject : Mathematics  Document Language : English  Abstract : Let X, Y be Banach spaces and let us denote by C(S, X) the space of all X-valued continuous functions on the compact Hausdorff space S, equipped with the uniform norm. We shall write C(S, X) = C(S) if X = ℝ or ℂ. Now, consider a bounded linear operator T: C(S, X) → Y and assume that, due to the effect of a change of variable performed by a bounded operator V: C(S, X) → C(S), the operator T takes the product form T = θ·V, with θ: C(S) → Y linear and bounded. In this paper, we prove some integral formulas giving the representing measure of the operator T, which appeared as an essential object in integral representation theory. This is made by means of the representing measure of the operator 9 which is generally easier. Essentially the estimations are of the Radon-Nikodym type and precise formulas are stated for weakly compact and nuclear operators.  ISSN : 0862-9544  Journal Name : Acta Mathematica Universitatis Comenianae  Volume : 74  Issue Number : 1  Publishing Year : 1426 AH 2005 AD  Article Type : Article  Added Date : Saturday, December 31, 2011  Researchers Researcher Name (Arabic) Researcher Name (English) Researcher Type Dr Grade Email لخضر مزياني Meziani, Lakhdar Researcher Doctorate mezianilakhdar@hotmail.com Files File Name Type Description  31869.pdf pdf Abstract Back To Researches Page