Operators with compatible ranges

2016/09/15 by Djikić, Marko S.
#15A09 #47A05 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1609.04884

Abstract

A bounded operator T on a finite or infinite--dimensional Hilbert space is called a disjoint range (DR) operator if R(T)∩ R(T^*)=\0\, where T^* stands for the adjoint of T, while R(⋅) denotes the range of an operator. Such operators (matrices) were introduced and systematically studied by Baksalary and Trenkler, and later by Deng et al. In this paper we introduce a wider class of operators: we say that T is a compatible range (CoR) operator if T and T^* coincide on R(T)∩ R(T^*). We extend and improve some results about DR operators and derive some new results regarding the CoR class.

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