<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE ArticleSet PUBLIC "-//NLM//DTD PubMed 2.6//EN" "http://www.ncbi.nlm.nih.gov/corehtml/query/static/PubMed.dtd">
<ArticleSet>
<Article>
<Journal>
				<PublisherName>Iranian Mathematical Society (IMS)</PublisherName>
				<JournalTitle>Bulletin of the Iranian Mathematical Society</JournalTitle>
				<Issn>1017-060X</Issn>
				<Volume></Volume>
				<Issue>Articles in Press</Issue>
				<PubDate PubStatus="epublish">
					<Year>2011</Year>
					<Month>06</Month>
					<Day>20</Day>
				</PubDate>
			</Journal>
<ArticleTitle>C-frames and c-bessel mappings</ArticleTitle><FirstPage></FirstPage>
			<LastPage></LastPage>
			<Language>en</Language>
<AuthorList>
<Author>
					<FirstName>Mohammad Hasan </FirstName>
					<LastName>Faroughi</LastName>
					<Affiliation>Islamic Azad University - Shabestar Branch</Affiliation>
				</Author>
<Author>
					<FirstName>Elnaz </FirstName>
					<LastName>Osgooei</LastName>
					<Affiliation>University of Tabriz</Affiliation>
				</Author>
</AuthorList>
			<History>
				<PubDate PubStatus="received">
					<Year>2011</Year>
					<Month>06</Month>
					<Day>07</Day>
				</PubDate>
			</History>
		<Abstract><![CDATA[The theory of c-frames and c-Bessel mappings are the generalizations
of the theory of frames and Bessel sequences. In this article, we
obtain several equivalence conditions for dual of c-Bessel mappings.
We show that for a c-Bessel mapping $f$, an retrieval
formula with respect to a c-Bessel mapping $g$ is satisfied if and
only if $g$ is sum of the canonical dual of $f$ with a c-Bessel
mapping which is weakly in the null space of the pre-frame operator
of $f$. Also, we prove that composition of pre-frame operator with
analysis operator of two square norm integrable c-Bessel mappings
are trace class operators.]]></Abstract>
		<ObjectList>
			<Object Type="keyword">
			<Param Name="value">Lebesque integral</Param>
			</Object>
			<Object Type="keyword">
			<Param Name="value">Hilbert space</Param>
			</Object>
			<Object Type="keyword">
			<Param Name="value">$C^*$-algebra</Param>
			</Object>
			<Object Type="keyword">
			<Param Name="value">trace class operator</Param>
			</Object>
			<Object Type="keyword">
			<Param Name="value">frame theory</Param>
			</Object>
		</ObjectList>
</Article>
</ArticleSet>