Abstract
Although the theory of completion has a long history, there are not many results related to completing operator matrices to a normal operator. In this paper, we consider the problem of completion of the upper-triangular operator matrix [A?0B⁎] to normality, where A∈B(H) and B∈B(K) are called normal complements. We give different characterizations of normal complements and explore their joint spectral properties. We also investigate the similarity between A, B, and MC with respect to some essential properties such as regularity, Fredholmness, and others. Finally, we consider the self-duality property of Aluthge and Duggal transforms of hyponormal and semi-hyponormal operators.
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