Elementary Properties of Hyponormal Operators and Semi-Hyponormal Operators
Daoxing Xia · Operator theory · 1983
The spectral analysis of operators has always been one of the interesting and active topics of Operator Theory. The theory of spectral analysis of self-adjoint operators, unitary and normal operators is now an important part of the many textbooks on Functional Analysis. Since the 1950’s, many mathematicians have considered more general linear operators. Various theories have appeared. For example, the spectral operator theory (DUNFORD & SCHWARTZ [1]), the generalized spectral operator theory (COLOJOARĂ & FOIAŠ [1]), the theory of non-selfadjoint operators (BRODSKIǏ [1], GOHBERG & KREIN [1,2]), the harmonic analysis of contractions (SZ-NAGY & FOIAŠ [1]), the theory of invariant subspaces (RADJAVI & ROSENTHAL [1]), the theory of hyponormal, semihyponormal and nearly normal operators, which is the main subject studied in this book. Some of these theories were inspired by the spectral analysis of self-adjoint operators, unitary operators and normal operators. All these new developments are important, interesting and very useful. New methods have been presented, various difficulties overcome and new applications obtained. Of course, their application ranges are still limited. These theories have just been brought forth. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.