The spectra of unbounded hyponormal operators

Author:
C. R. Putnam

Journal:
Proc. Amer. Math. Soc. **31** (1972), 458-464

MSC:
Primary 47B20

DOI:
https://doi.org/10.1090/S0002-9939-1972-0291848-8

MathSciNet review:
0291848

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: A bounded operator on a Hilbert space is said to be completely hyponormal if and if has no nontrivial reducing space on which it is normal. If 0 is in the spectrum of such an operator and if the spectrum of near 0 is not ``too dense,'' then the unbounded operator acts as though it were bounded. In particular, under certain conditions, has a rectangular representation with absolutely continuous real and imaginary parts whose spectra are the closures of the projections of the spectrum of onto the coordinate axes.

**[1]**K. F. Clancey,*Spectral properties of semi-normal operators*, Thesis, Purdue University, Lafayette, Ind., 1969.**[2]**C. R. Putnam,*On the spectra of semi-normal operators*, Trans. Amer. Math. Soc.**119**(1965), 509-523. MR**32**#2913. MR**0185446 (32:2913)****[3]**-,*Commutation properties of Hilbert space operators and related topics*, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 36, Springer-Verlag, New York, 1967. MR**36**#707. MR**0217618 (36:707)****[4]**-,*An inequality for the area of hyponormal operators*, Math. Z.**116**(1970), 323-330. MR**0270193 (42:5085)****[5]**C. R. Putnam,*Unbounded inverses of hyponormal operators*, Pacific J. Math.**35**(1970), 755-762. MR**0275214 (43:971)****[6]**-,*A similarity between hyponormal and normal spectra*, Illinois J. Math. (to appear). MR**0326462 (48:4806)****[7]**J. G. Stampfli,*Hyponormal operators and spectral density*, Trans. Amer. Math. Soc.**117**(1965), 469-476. MR**30**#3375. MR**0173161 (30:3375)****[8]**-,*Analytic extensions and spectral localization*, J. Math. Mech.**16**(1966), 287-296. MR**33**#4687. MR**0196500 (33:4687)****[9]**M. H. Stone,*Linear transformations in Hilbert space and their applications to analysis*, Amer. Math. Soc. Colloq. Publ., vol. 15, Amer. Math. Soc., Providence, R.I., 1932. MR**1451877 (99k:47001)**

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC:
47B20

Retrieve articles in all journals with MSC: 47B20

Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1972-0291848-8

Keywords:
Hyponormal operators,
absolutely continuous operators

Article copyright:
© Copyright 1972
American Mathematical Society