The Fuglede-Putnam Theorem and Quasinormality for Class p-wA(s, t) Operators

Authors

  • Mohammad H.M. Rashid Mu'tah University
  • N.H. Altaweel Department of Mathematics-Faculty of Science-University of Tabuk

DOI:

https://doi.org/10.29020/nybg.ejpam.v15i3.4412

Keywords:

Fuglede-Putnam theorem, Class $p$-$(A(s,t)$ operators, Class $A(s,t)$ operators, quasinormal

Abstract

In this work, we demonstrate that (i) if T is a class p-wA(s, t) operator and T(s, t) is quasinormal (resp., normal), then T is also quasinormal (resp., normal) (ii) If T and T∗ are class p-wA(s, t) operators, then T is normal; (iii) the normal portions of quasisimilar class p-wA(s, t) operators are unitarily equivalent; and (iv) Fuglede-Putnam type theorem holds for a class p-wA(s, t) operator T for 0< s, t, s + t = 1 and 0 < p ≤ 1 if T satisfies a kernel condition ker(T) ⊂ ker(T∗).

Author Biography

Mohammad H.M. Rashid, Mu'tah University

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How to Cite

Rashid, M. H., & Altaweel, N. . (2022). The Fuglede-Putnam Theorem and Quasinormality for Class p-wA(s, t) Operators. European Journal of Pure and Applied Mathematics, 15(3), 1067–1089. https://doi.org/10.29020/nybg.ejpam.v15i3.4412