PUBLICATIONS DE L'INSTITUT MATHÉMATIQUE (BEOGRAD) (N.S.) Vol. 29(43), pp. 513 (1981) 

$M$  PARANORMAL OPERATORSS.C. Arora and Ramesh KumarDepartment of Mathematics, Hans Raj College, University of Delhi, Delhi 11007, India and Department of Mathematics, Khalsa College, University of Delhi, Delhi 11007, IndiaAbstract: V. Istratescu has recently defined $M$paranormal operators on a Hilbert space $H$ as: An operator $T$ is called $M$paranormal if for all $x\in H$ with $\x\=1$, $$ \T^2 x\\geqq\frac1M\Tx\^2 $$ We prove the following results: \item{1.} $T$ is $M$paranormal if and only if $M^2T^*2T^22\lambda T^*T+\lambda^2 \geq 0$ for all $\lambda > 0$. \item{2.} If a $M$paranormal operator $T$ double commutes with a hyponormal operator $S$, then the product $TS$ is $M$paranormal. \item{3.} If a paranormal operator $T$ doble commutes with a $M$hyponormal operator, then the product $TS$ is $M$paranormal. \item{4.} If $T$ is invertible $M$paranormal, then $T^{1}$ is also $M$paranormal. \item{5.} If $Re W (T) \leq 0$, where $W (T)$ denotes the numerical range of $T$, then $T$ is $M$paranormal for $M \geq 8$. \item{6.} If a $M$paranormal partial isometry $T$ satisfies $\T\ \leq \frac1M$, then it is subnormal. Full text of the article:
Electronic fulltext finalized on: 3 Nov 2001. This page was last modified: 16 Nov 2001.
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