The role of zero sets in the spectra of hyponormal operators

Author:
C. R. Putnam

Journal:
Proc. Amer. Math. Soc. **43** (1974), 137-140

MSC:
Primary 47B20

MathSciNet review:
0333808

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Abstract: A compact set in the complex plane is the spectrum of a completely hyponormal operator if and only if the set has positive density.

**[1]**K. F. Clancey and C. R. Putnam,*The local spectral behavior of completely subnormal operators*, Trans. Amer. Math. Soc.**163**(1972), 239–244. MR**0291844**, 10.1090/S0002-9947-1972-0291844-5**[2]**K. F. Clancey and C. R. Putnam,*The spectra of hyponormal integral operators*, Comment. Math. Helv.**46**(1971), 451–456. MR**0301573****[3]**Richard Darst and Casper Goffman,*A Borel set which contains no rectangles*, Amer. Math. Monthly**77**(1970), 728–729. MR**0264016****[4]**R. O. Davies,*On accessibility of plane sets and differentiation of functions of two real variables*, Proc. Cambridge Philos. Soc.**48**(1952), 215–232. MR**0045795****[5]**C. R. Putnam,*An inequality for the area of hyponormal spectra*, Math. Z.**116**(1970), 323–330. MR**0270193****[6]**C. R. Putnam,*The spectra of completely hyponormal operators*, Amer. J. Math.**93**(1971), 699–708. MR**0281038**

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DOI:
https://doi.org/10.1090/S0002-9939-1974-0333808-6

Keywords:
Hyponormal operator,
subnormal operator,
spectrum

Article copyright:
© Copyright 1974
American Mathematical Society