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Some conditions on an operator implying normality. (English) Zbl 0176.11301


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[1] Ando, T.: On hyponormal operators. Proc. Amer. Math. Soc.14, 290-291 (1963). · Zbl 0113.09904 · doi:10.2307/2034629
[2] Berberian, S. K.: Introduction to Hilbert space. New York: Oxford University Press 1961. · Zbl 0121.09302
[3] Bernau, S., Smithies, F.: A note on normal operators. Proc. Cambridge Philos. Soc.59, 727-729 (1963). · Zbl 0161.34901 · doi:10.1017/S0305004100003728
[4] Douglas, R. G., Rosenthal, P.: A necessary and sufficient condition that an operator be normal. J. Math. Anal. Appl.22, 10-11 (1968). · Zbl 0155.46104 · doi:10.1016/0022-247X(68)90155-8
[5] Halmos, P. R.: A Hilbert space problem book. Princeton, N.J.: Van Nostrand 1967. · Zbl 0144.38704
[6] Hildebrandt, S.: Über den numerischen Wertebereich eines Operators. Math. Ann.163, 230-247 (1966). · Zbl 0138.39101 · doi:10.1007/BF02052287
[7] Lorch, E. R.: Spectral theory. New York: Oxford University Press 1962. · Zbl 0151.19702
[8] Riesz, F., Sz.-Nagy, B.: Leçons d’analyse fonctionelle. Budapest: Akadémiai Kiadó 1952.
[9] Saitô, T., Yoshino, T.: On a conjecture of Berberian. Tôhoku Math. J.17, 147-149 (1965). · Zbl 0132.35703 · doi:10.2748/tmj/1178243580
[10] Stampfli, J. G.: Hyponormal operators. Pacific J. Math.12, 1453-1458 (1962). · Zbl 0129.08701
[11] ?? Minimal range theorems for operators with thin spectra. Pacific J. Math.23, 601-612 (1967). · Zbl 0152.33802
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