IJPAM: Volume 104, No. 4 (2015)

GENERALIZATION OF $m$-PARTIAL ISOMETRIES
ON A HILBERT SPACE

Ould Ahmed Mahmoud Sid Ahmed
Department of Mathematics
College of Science
Aljouf University
Al Jouf, 2014, SAUDI ARABIA


Abstract. In this paper we introduce a generalization of the class of $m$-partial isometries operators recently studied in $ [24].$ A bounded linear operator $T$ on a Hilbert space $\mathcal{H}$ is called an $m$- partial isometry of order $q$ for a positive integers $m$ and $q$, if

\begin{displaymath} T^q\Bigg( T^{*m}T^{m}- \binom{m}{1}T^{*m-1}T^{m-1}+ \binom{m}{2} T^{*m-2}T^{m-2}-\cdots+(-1)^mI\Bigg)=0. \end{displaymath}



Received: August 8, 2015

AMS Subject Classification: 47B48

Key Words and Phrases: Hilbert space, isometry, partial isometry, $m$-isometric operator, reducing subspace, the single valued extension property

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DOI: 10.12732/ijpam.v104i4.11 How to cite this paper?

Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2015
Volume: 104
Issue: 4
Pages: 599 - 619


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