A note on elementary operators on the Calkin algebra

Gravner, Janko

doi:10.1090/S0002-9939-1986-0831392-X

A note on elementary operators on the Calkin algebra

Author: Janko Gravner
Journal: Proc. Amer. Math. Soc. 97 (1986), 79-86
MSC: Primary 47A10; Secondary 47A53, 47C05, 47D25
DOI: https://doi.org/10.1090/S0002-9939-1986-0831392-X
MathSciNet review: 831392
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Various parts of the spectrum of elementary operators on the Calkin algebra are characterised by means of the joint (Harte) spectra of -tuples of operators.

[1] W. Arveson, Notes on extensions of ${C^*}$ -algebras, Duke Math. J. 44 (1977), 329-355. MR 0438137 (55:11056)
[2] A. Carrillo and C. Hernandez, Spectra of constructs of a system of operators, Proc. Amer. Math. Soc. 91 (1984), 426-432. MR 744643 (85f:47016)
[3] A. T. Dash, Joint essential spectra, Pacific J. Math. 64 (1976), 119-128. MR 0425641 (54:13595)
[4] L. A. Fialkow, A note on the operator $X \to AX - AB$ , Trans. Amer. Math. Soc. 243 (1978), 147-168. MR 502900 (80c:47017)
[5] -, Spectral properties of elementary operators, Acta Sci. Math. (Szeged) 46 (1983), 269-282. MR 739043 (85h:47003)
[6] -, Spectral properties of elementary operators.II, (preprint).
[7] P. A. Fillmore, J. G. Stampfli and J. P. Williams, On the essential numerical range, esssential spectrum and a problem of Halmos, Acta Sci. Math. (Szeged) 33 (1972), 179-192. MR 0322534 (48:896)
[8] C. K. Fong and A. R. Sorour, On the operator identity $\sum {{A_k}X{B_k} \equiv 0}$ , Canad. J. Math. 31 (1979), 845-857.
[9] R. E. Harte, Spectral mapping theorems, Proc. Roy. Irish Acad. Sect. A 72 (1972), 89-107. MR 0326394 (48:4738)
[10] -, Spectral mapping theorems for quasicommuting systems, Proc. Roy. Irish Acad. Sect. A 73 (1973), 7-18. MR 0318880 (47:7426)
[11] -, Tensor products, multiplication operators and the spectral mapping theorems, Proc. Roy. Irish Acad. Sect. A 73 (1973), 285-302. MR 0328642 (48:6984)
[12] G. Lumer and M. Rosenblum, Linear operator equations, Proc. Amer. Math. Soc. 10 (1959), 32-41. MR 0104167 (21:2927)
[13] M. Mathieu, Spectral theory for multiplication operators on ${C^*}$ -algebras, Proc. Roy. Irish Acad. Sect. A 83 (1983), 231-249. MR 736499 (85m:46055)
[14] D. Voiculescu, A non-commutative Weyl-von Neumann theorem, Rev. Roumaine Math. Pures Appl. 21 (1976), 97-113. MR 0415338 (54:3427)
[15] R. E. Weber, On weak*-continuous operators on $\mathcal{L}(\mathcal{H})$ , Proc. Amer. Math. Soc. 83 (1981), 735-742. MR 630046 (82j:47003)