A characterization of the Browder spectrum

Author:
Norberto Salinas

Journal:
Proc. Amer. Math. Soc. **38** (1973), 369-373

MSC:
Primary 47A55

MathSciNet review:
0313852

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Several different notions of essential spectra are known. This paper is devoted to giving an equivalent definition of the *Browder* essential spectrum for bounded operators on Hilbert space. Also, it is shown that the set of all operators with essentially disconnected spectrum is a uniformly dense set.

**[1]**S. K. Berberian,*The Weyl spectrum of an operator*, Indiana Univ. Math. J.**20**(1970/1971), 529–544. MR**0279623****[2]**Felix E. Browder,*On the spectral theory of elliptic differential operators. I*, Math. Ann.**142**(1960/1961), 22–130. MR**0209909****[3]**Arlen Brown, Carl Pearcy, and Norberto Salinas,*Perturbations by nilpotent operators on Hilbert space*, Proc. Amer. Math. Soc.**41**(1973), 530–534. MR**0374955**, 10.1090/S0002-9939-1973-0374955-1**[4]**I. C. Gohberg and M. G. Kreĭn,*Introduction to the theory of linear nonselfadjoint operators*, Translated from the Russian by A. Feinstein. Translations of Mathematical Monographs, Vol. 18, American Mathematical Society, Providence, R.I., 1969. MR**0246142****[5]**Domingo A. Herrero and Norberto Salinas,*Operators with disconnected spectra are dense*, Bull. Amer. Math. Soc.**78**(1972), 525–526. MR**0301535**, 10.1090/S0002-9904-1972-12981-1**[6]**Roger D. Nussbaum,*Spectral mapping theorems and perturbation theorems for Browder’s essential spectrum*, Trans. Amer. Math. Soc.**150**(1970), 445–455. MR**0265967**, 10.1090/S0002-9947-1970-0265967-9**[7]**Norberto Salinas,*Operators with essentially disconnected spectrum*, Acta Sci. Math. (Szeged)**33**(1972), 193–205. MR**0350450****[8]**Martin Schechter,*Invariance of the essential spectrum*, Bull. Amer. Math. Soc.**71**(1965), 365–367. MR**0174979**, 10.1090/S0002-9904-1965-11296-4**[9]**Joseph G. Stampfli,*Compact perturbations, normal eigenvalues and a problem of Salinas*, J. London Math. Soc. (2)**9**(1974/75), 165–175. MR**0365196****[10]**František Wolf,*On the invariance of the essential spectrum under a change of boundary conditions of partial differential boundary operators*, Nederl. Akad. Wetensch. Proc. Ser. A 62 = Indag. Math.**21**(1959), 142–147. MR**0107751**

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC:
47A55

Retrieve articles in all journals with MSC: 47A55

Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1973-0313852-4

Keywords:
Compression to subspaces of finite codimension,
polynomial hull of the Browder spectrum

Article copyright:
© Copyright 1973
American Mathematical Society