Fuglede-Putnam type theorems for extension of $\ast$-class $A$ operators

نویسندگان
Rashid, Mohammad ID 1

1 Department of Mathematics & Statistics, Faculty of Science, P.O.Box 7, Mu'tah University, Al-Karak, Jordan

doi
10.22075/ijnaa.2021.21260.2243
چکیده

In this article, we consider $k$-quasi-$\ast$-class $A$ operator $T\in\bh$ such that $TX=XS$ for some $X\in \bkh$ and prove the Fuglede-Putnam type  theorem when adjoint of $S\in\bk$ is $k$-quasi-$\ast$-class $A$ or dominant operators. Among other things, we prove that two quasisimilar  $k$-quasi-$\ast$-class $A$ operators have equal essential spectra.   

کلیدواژه‌ها
$ast$-class $A$ operators, $k$-quasi-$ast$-class $A$ operators, quasisimilar operators