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arXiv · 1609.04884

Operators with compatible ranges

Marko S. Djikić
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Abstract

A bounded operator $T$ on a finite or infinite--dimensional Hilbert space is called a disjoint range (DR) operator if $R(T)\cap R(T^*)=\{0\}$, where $T^*$ stands for the adjoint of $T$, while $R(\cdot)$ 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 $R(T)\cap R(T^*)$. We extend and improve some results about DR operators and derive some new results regarding the CoR class.

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Marko S. Djikić. 2016-09-15. Operators with compatible ranges. https://arxiv.org/abs/1609.04884

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