On the Existence of Normal Square and Nth Roots of Operators

2018/01/21 by Mortad, Mohammed Hichem
#47A62 #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.1801.06884

Abstract

The primary purpose of this paper is to show the existence of normal square and nth roots of some classes of bounded operators on Hilbert spaces. Two interesting simple results hold. Namely, under simple conditions we show that if any operator T is such that T²=0, then this implies that T is normal and so T=0. Also, we will see when the square root of an arbitrary bounded operator is normal.

Related

• On nth roots of normal operators
• Some inequalities for (α, β)-normal operators in Hilbert spaces
• Unbounded operators having self-adjoint or normal powers and some related results
• Certain properties involving the unbounded operators p(T), TT^*, and T^*T; and some applications to powers and nth roots of unbounded operators
• Operator inequalities and characterizations