Some characterizations of Hermitian operators and related classes of operators. I

Authors:
Che Kao Fong and Vasile I. Istrăţescu

Journal:
Proc. Amer. Math. Soc. **76** (1979), 107-112

MSC:
Primary 47B20

DOI:
https://doi.org/10.1090/S0002-9939-1979-0534398-X

MathSciNet review:
534398

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Abstract | References | Similar Articles | Additional Information

Abstract: It is shown that, among other things, an operator *T* is hermitian if and only if . Also, the class of those operators *T* satisfying is investigated.

**[1]**S. L. Campbell,*Linear operators for which**and**commute*, Pacific J. Math.**61**(1975), 53-57. MR**0405168 (53:8963)****[2]**-,*Operator-valued inner functions analytic on the closed unit disc*. II, Pacific J. Math.**60**(1975), 37-50.**[3]**S. L. Campbell and R. Gellar,*Spectral properties of linear operators which**and**commute*, Proc. Amer. Math. Soc.**60**(1976), 197-202. MR**0417841 (54:5889)****[4]**-,*Linear operators for which**and**commute*. II, Trans. Amer. Math. Soc.**226**(1977), 305-319. MR**0435905 (55:8856)****[5]**P. R. Halmos,*A Hilbert space problem book*, Van Nostrand, Princeton, N.J., 1967. MR**0208368 (34:8178)****[6]**V. I. Istrăţescu,*On some hyponormal operators*, Pacific J. Math.**22**(1967), 413-417. MR**0213893 (35:4747)****[7]**-,*Topics in linear operator theory*, Accademia Nazionale dei Lincei, Roma, 1978.**[8]**C. R. Putnam,*On the spectra of semi-normal operators*, Trans. Amer. Math. Soc.**119**(1965), 509-523. MR**0185446 (32:2913)****[9]**M. Radjabalipour,*On normality of operators*, Indiana Univ. Math. J.**23**(1974), 623-630. MR**0326480 (48:4824)****[10]**A. E. Taylor,*Theorems on ascent, descent, nullity and defect of linear operators*, Math. Ann.**163**(1966), 18-49. MR**0190759 (32:8169)**

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1979-0534398-X

Keywords:
Hermitian operator,
hyponormal operator,
real part of an operator,
class (WN),
spectrum

Article copyright:
© Copyright 1979
American Mathematical Society