Abstract
If A 1, A 2..., Type="Italic">A n are mutually commuting linear operators on Hilbert space H, then the joint spectrum Sp(A) for n-tuple A = (A 1, A 2,...; ...;,A n) can be defined in terms of the Kaszul complex by J. L. Taylor [1]. Since 1982, we have tried to generalize the results on the spectrum properties of a single operator to the case of joint spectrum for n-tuple of linear operators [2]. This article is a ten years survey for this subject.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Taylor, J. L., A joint spectrum for several commuting operators, J. Funct. Anal., 19(1975), 390–421.
Zhang Dianzhou et al., Joint spectrum for n-tuple of linear operators (in Chinese), East China Normal University Press, Shanghai, (1992), 1–262.
Zhang Dianzhou and Huang Danren, On the joint spectrum for n-tuple of hyponomal operators, Chinese Annals of Mathematics, 7b, 1(1986), 14–23.
Xia, D., Spectral Theory of Linear Operator (I), (in Chinese), Academy Press, Beijing, 1983.
Hu Shanwen, Theory of Joint Spectrum, Dissertation, Fudan University, Shanghai, (1988).
Eschmeier, J., Spektralzerlegungen und Functionakakule für vertauschende tupel stetiger und abgeschlossener Operator in Banachraumen, Schriftenreine des Mathematika, Instituts der Universität Münster, 2. serie, helf 20, Juli, (1981), 1045.
Zhang Dianzhou and Wang Zongyao, Talor joint spectrum for n-tuple of closed operators on Hilbert space, Scientia Scinica, Series A, 6(1985).
Huang Danren and Zhang Dianzhou, Joint spectrum and unbounded operator algebras, Acta Matimatica, 3, 2(1986).
Inoue, A., On a class of unbounded operator algebras, Pacific J. Math., 65(1976), 77–95.
Allan. G. R., On a class of locally convex algebras, Proc. London Math. Soc., 3, 17(1967), 91–114.
Hu Shanwen, Joint essential spectrum and index of tensor product of linear operators in Banach spaces, Kexue Tongbao, 11, 34(1989), 885–888.
Huang Danren, On the joint spectrum for n-tuple of linear operators and its applications, Dissertation (Master degree), East China Normal University, (1984).
Cai Jun, A classification of joint spctrum and perbutations, Dissertation (Master degree), East China Normal University, (1984).
Huang Danren, Joint numerical ranges for unbounded normal operators, Proc. Edinburgh Math. Soc., 28(1985), 225–232.
Hu Shanwen, Commuting n-tuple of closed operators which posses spectral capacity, Chinese Annals of Mathematics, 2, 8B, (1987), 156–159.
Curto, R. E., Fredholm and invertible n-tuples of operators, Tran. Math. Soc., 226(1981), 129–159.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1996 Kluwer Academic Publishers
About this chapter
Cite this chapter
Zhang, D. (1996). Some Results on the Joint Spectrum for N — Tuple of Linear Operators. In: Li, B., Wang, S., Yan, S., Yang, CC. (eds) Functional Analysis in China. Mathematics and Its Applications, vol 356. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-0185-8_21
Download citation
DOI: https://doi.org/10.1007/978-94-009-0185-8_21
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-6567-2
Online ISBN: 978-94-009-0185-8
eBook Packages: Springer Book Archive