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

Document Type : Research Paper

Author

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

Abstract

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.   

Keywords

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Volume 13, Issue 2
July 2022
Pages 863-873
  • Receive Date: 02 September 2020
  • Revise Date: 17 November 2020
  • Accept Date: 12 April 2021