Hostname: page-component-cd9895bd7-gvvz8 Total loading time: 0 Render date: 2024-12-23T02:17:58.112Z Has data issue: false hasContentIssue false

Joint Browder spectra and tensor products

Published online by Cambridge University Press:  17 April 2009

A.T. Dash
Affiliation:
Department of Mathematics and Statistics, College of Physical Science, University of Guelph, Guelph, Ontario, CanadaNIG 2WI.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

There exists in the literature several notions of joint spectra which can be generalized to joint Browder spectra. The purpose of this note is to show that various notions of joint Browder spectra coincide for a special class of operators.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1985

References

[1]Arveson, W., “Subalgebras of C*-algebras II”, Acta Math. 128 (1972), 271308.CrossRefGoogle Scholar
[2]Berberian, S.K., “The Weyl spectrum of an operator”, Indiana Univ. Math. J. 20 (1970), 529544.CrossRefGoogle Scholar
[3]Browder, F.E., “On the spectral theory of elliptic differential operators I”, Math. Ann. 142 (1961), 22130.CrossRefGoogle Scholar
[4]Buoni, J.J., Dash, A.T. and Wadhaw, B.L., “Joint Browder spectrum”, Pacific J. Math. 94 (1981), 259263.CrossRefGoogle Scholar
[5]Ceausescu, Z. and Vasilescu, F.-H., “Tensor products and Taylor's joint spectrum”, Studia Math. 62 (1978), 305311.CrossRefGoogle Scholar
[6]Curto, R.E., “Fredholm and invertible n-tuples of operators. The deformation problem”, Trans. Amer. Math. Soc. 266 (1981), 129159.Google Scholar
[7]Dash, A.T., “Joint spectra”, Studia Math. 45 (1973), 225237.CrossRefGoogle Scholar
[8]Dash, A.T., “Joint essential spectra”, Pacific J. Math. 64 (1976), 119128.CrossRefGoogle Scholar
[9]Dash, A.T., “On a conjecture concerning joint spectra”, J. Funct. Anal. 6 (1970), 165171.CrossRefGoogle Scholar
[10]Dash, A.T. and Schechter, M., “Tensor products and joint spectra”, Israel J. Math. 8 (1970), 191193.CrossRefGoogle Scholar
[11]Filmore, P.A., Stampfli, J.G. and Williams, J.P., “On the essential numerical range, the essential spectrum and a problem of Halmos”, Acta Sci. Math. Szeged 33 (1972), 179192.Google Scholar
[12]Schechter, M. and Snow, M., “The Fredholm spectrum of tensor products”, Proc. Roy. Irish Acad. Sect. A 75 (1975), 121128.Google Scholar
[13]Snow, M., “A joint Browder essential spectrum”, Proc. Roy. Irish Acad. Sect. A 75 (1975), 129131.Google Scholar
[14]Taylor, J.L., “A joint spectrum for several commuting operators”, J. Funct. Anal. 6 (1970), 172191.CrossRefGoogle Scholar
[15]Vasilescu, F.-H., “A characterization of joint spectrum in Hilbert spaces”, Rev. Roumaine Math. Pures Appl. 22 (1977), 10031009.Google Scholar