%------------------------------------------------------------------------------ % Beginning of journal.tex %------------------------------------------------------------------------------ % \documentclass[12pt, reqno]{amsart} \usepackage{amsmath, amsthm, amscd, amsfonts, amssymb, graphicx, color} \usepackage[bookmarksnumbered, plainpages]{hyperref} \textheight 22.5truecm \textwidth 14.5truecm \setlength{\oddsidemargin}{0.35in}\setlength{\evensidemargin}{0.35in} \setlength{\topmargin}{-.5cm} \newtheorem{theorem}{Theorem}[section] \newtheorem{lemma}[theorem]{Lemma} \newtheorem{proposition}[theorem]{Proposition} \newtheorem{corollary}[theorem]{Corollary} \theoremstyle{definition} \newtheorem{definition}[theorem]{Definition} \newtheorem{example}[theorem]{Example} \newtheorem{xca}[theorem]{Exercise} \newtheorem{problem}[theorem]{Problem} \theoremstyle{remark} \newtheorem{remark}[theorem]{Remark} \numberwithin{equation}{section} \newtheorem*{t1}{Theorem I} \newtheorem*{t2}{Theorem II} \newtheorem*{t3}{Theorem III} \numberwithin{equation}{section} \newcommand{\R}{\mathbb{R}} \newcommand{\ran}{\text{\rm{ran}}} \begin{document} \setcounter{page}{40} \noindent\parbox{2.85cm}{\includegraphics*[keepaspectratio=true,scale=1.75]{BJMA.jpg}} \noindent\parbox{4.85in}{\hspace{0.1mm}\\[1.5cm]\noindent Banach J. Math. Anal. 2 (2008), no. 1, 40--47\\ $\frac{\rule{4.55in}{0.05in}}{{}}$\\ {\footnotesize \textcolor[rgb]{0.65,0.00,0.95}{\textsc{\textbf{\large{B}}anach \textbf{\large{J}}ournal of \textbf{\large{M}}athematical \textbf{\large{A}}nalysis}}\\ ISSN: 1735-8787 (electronic)\\ \textcolor[rgb]{0.00,0.00,0.84}{\textbf{http://www.math-analysis.org }}\\ $\frac{{}}{\rule{4.55in}{0.05in}}$}\\[.5in]} \title[Products of Closed Operators]{On Different Products of Closed Operators} \author[B. Messirdi, M.H. Mortad]{BEKKAI MESSIRDI$^1$ and MOHAMMED HICHEM MORTAD$^2$ $^{*}$} \address{$^{1}$ D\'{e}partement de Math\'{e}matiques, Universit\'{e} d'Oran (Es-senia), B.P. 1524, El Menouar, Oran 31000, Algeria.} \email{\textcolor[rgb]{0.00,0.00,0.84}{bmessirdi@univ-oran.dz, bmessirdi@yahoo.fr.}} \address{$^{2}$ D\'{e}partement de Math\'{e}matiques, Universit\'{e} d'Oran (Es-senia), B.P. 1524, El Menouar, Oran 31000, Algeria.} \email{\textcolor[rgb]{0.00,0.00,0.84}{mortad{\_}maths@yahoo.com, mortad@univ-oran.dz.}} \dedicatory{{\rm Submitted by H. Dedania}} \subjclass[2000]{47A05.} \keywords{Closed operator, product, Hilbert space.} \date{Received: 26 December 2007; Accepted: 9 April 2008. \newline \indent $^{*}$ Corresponding author} \begin{abstract} The purpose of this work is to give different products of closed operators together with their faults and assets. \end{abstract} \maketitle \vspace{2in} \end{document} .