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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
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