اخي هذا موضوع طويل يطول شرحه
راجع هذه الكتب
A Hilbert Space Problem Book, by Halmos
N. DUNFORD AND J. SCHWARTZ, Linear Operators I, II, III
Analysis of Non-normal Operators via Aluthge Transformation, by Fumihiko Kimura
D. Xia, Spectral Theory of Hyponormal Operators, Birkhiuser Verlag, Boston, 1983.
وهذه البحوث مفيدة كمان
I. C. GOHBERG AND M. G. KREIN, Introduction to the Theory of Linear Nonselfadjoint Operators
American Mathematical Society, Providence, RI, 1969
J.G. Stampfli, Hyponormal operators, Pacific J. Math., 12 (1962), 1453-1458.
J.G. Stampfli, Hyponormal operators and spectral density, Trans. Amer. Math. Soc.,
117 (1965), 469-476.
D. Xia, On the nonnormal operators-semihyponormal operators, Sci. Sininca, 23
(1980), 700-713.