A representation of hyponormal absolutely norm attaining operators. (English) Zbl 1487.47008
Summary: In this article, we characterize absolutely norm attaining normal operators in terms of the essential spectrum. Later we prove a structure theorem for hyponormal absolutely norm attaining (or \(\mathcal{AN}\)-operators in short) and deduce conditions for the normality of the operator.
MSC:
| 47A10 | Spectrum, resolvent |
| 47B15 | Hermitian and normal operators (spectral measures, functional calculus, etc.) |
| 47B20 | Subnormal operators, hyponormal operators, etc. |
| 47A65 | Structure theory of linear operators |
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