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Keywords:
Banach algebra; joint spectrum; subspectrum; spectroid; geometrical spectral radius; (joint) capacity
Banach algebra; joint spectrum; subspectrum; spectroid; geometrical spectral radius; (joint) capacity
Summary:
The aim of this paper is to characterize a class of subspectra for which the geometric spectral radius is the same and depends only upon a commuting $n$-tuple of elements of a complex Banach algebra. We prove also that all these subspectra have the same capacity.
References:
[1] Chō M., Takaguchi M.: Boundary points of joint numerical ranges. Pacific J. Math. 95 (1981), 27-35. MR 0631656
[2] Chō M., Żelazko W.: On geometric spectral radius of commuting $n$-tuples of operators. to appear in Hokkaido Math. J. MR 1169792
[3] Słodkowski Z., Żelazko W.: A note on semicharacters. in: Banach Center Publications, vol. 8, Spectral Theory, PWN, Warsaw, 1982, 397-402. MR 0738305
[4] Sołtysiak A.: Capacity of finite systems of elements in Banach algebras. Comment. Math. 19 (1977), 381-387. MR 0477779
[5] Sołtysiak A.: Some remarks on the joint capacities in Banach algebras. ibid. 20 (1978), 197-204. MR 0463939
[6] Stirling D.S.G.: The joint capacity of elements of Banach algebras. J. London Math. Soc. (2), 10 (1975), 212-218. MR 0370195 | Zbl 0302.46035
[7] Żelazko W.: An axiomatic approach to joint spectra I. Studia Math. 64 (1979), 249-261. MR 0544729
[8] Żelazko W.: Banach Algebras. Elsevier, PWN, Amsterdam, Warsaw, 1973. MR 0448079
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