Spectral pictures of and

Authors:
Robin Harte, Young Ok Kim and Woo Young Lee

Journal:
Proc. Amer. Math. Soc. **134** (2006), 105-110

MSC (2000):
Primary 47A10, 47A53, 47A66

Published electronically:
August 11, 2005

MathSciNet review:
2170549

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: The spectral pictures of products and of Banach space operators are compared; in particular when one of them is `of index zero'.

**[Al]**Ariyadasa Aluthge,*On 𝑝-hyponormal operators for 0<𝑝<1*, Integral Equations Operator Theory**13**(1990), no. 3, 307–315. MR**1047771**, 10.1007/BF01199886**[AFV]**Constantin Apostol, Ciprian Foiaş, and Dan Voiculescu,*Some results on non-quasitriangular operators. II, III, IV, V*, Rev. Roumaine Math. Pures Appl.**18**(1973), 159–181;ibid. 18 (1973), 309–324; ibid. 18 (1973), 487–514; ibid. 18 (1973), 1133–1149. MR**0333785****[Ba]**Bruce A. Barnes,*Common operator properties of the linear operators 𝑅𝑆 and 𝑆𝑅*, Proc. Amer. Math. Soc.**126**(1998), no. 4, 1055–1061. MR**1443814**, 10.1090/S0002-9939-98-04218-X**[BDF]**L. G. Brown, R. G. Douglas, and P. A. Fillmore,*Extensions of 𝐶*-algebras and 𝐾-homology*, Ann. of Math. (2)**105**(1977), no. 2, 265–324. MR**0458196****[Dj]**Dragan S. Djordjević,*Operators consistent in regularity*, Publ. Math. Debrecen**63**(2003), no. 1-2, 175–191. MR**1990872****[GGK]**Israel Gohberg, Seymour Goldberg, and Marinus A. Kaashoek,*Classes of linear operators. Vol. II*, Operator Theory: Advances and Applications, vol. 63, Birkhäuser Verlag, Basel, 1993. MR**1246332****[Ha]**Robin Harte,*Invertibility and singularity for bounded linear operators*, Monographs and Textbooks in Pure and Applied Mathematics, vol. 109, Marcel Dekker, Inc., New York, 1988. MR**920812****[JKP]**Il Bong Jung, Eungil Ko, and Carl Pearcy,*Spectral pictures of Aluthge transforms of operators*, Integral Equations Operator Theory**40**(2001), no. 1, 52–60. MR**1829514**, 10.1007/BF01202954**[LYR]**Chen Lin, Zikun Yan, and Yingbin Ruan,*Common properties of operators 𝑅𝑆 and 𝑆𝑅 and 𝑝-hyponormal operators*, Integral Equations Operator Theory**43**(2002), no. 3, 313–325. MR**1902952**, 10.1007/BF01255566**[Pe]**Carl M. Pearcy,*Some recent developments in operator theory*, American Mathematical Society, Providence, R.I., 1978. Regional Conference Series in Mathematics, No. 36. MR**0487495**

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC (2000):
47A10,
47A53,
47A66

Retrieve articles in all journals with MSC (2000): 47A10, 47A53, 47A66

Additional Information

**Robin Harte**

Affiliation:
School of Mathematics, Trinity College, Dublin, Ireland

Email:
rharte@maths.tcd.ie

**Young Ok Kim**

Affiliation:
Department of Mathematics, Seoul National University, Seoul 151-742, Korea

Email:
yhkim@skku.ac.kr

**Woo Young Lee**

Affiliation:
Department of Mathematics, Seoul National University, Seoul 151-742, Korea

Email:
wylee@math.snu.ac.kr

DOI:
http://dx.doi.org/10.1090/S0002-9939-05-08015-9

Keywords:
Spectral pictures,
index zero,
quasitriangular,
essentially normal operators,
compalent,
generalized Aluthge transforms

Received by editor(s):
November 7, 2003

Published electronically:
August 11, 2005

Additional Notes:
This work was supported by a grant (R14-2003-006-01000-0) from the Korea Science and Engineering Foundation, and by Enterprise Ireland Basic Research Grant SC/2002/0266

Communicated by:
David R. Larson

Article copyright:
© Copyright 2005
American Mathematical Society