Geodesic
Joint spectra of operators on Banach space
Glasgow mathematical journal, Tome 28 (1986) no. 1, pp. 69-72

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Let X be a complex Banach space. We denote by B(X) the algebra of all bounded linear operators on X. Let = (T1, ..., Tn) be a commuting n-tuple of operators on X. And let στ() and σ′′() by Taylor's joint spectrum and the doubly commutant spectrum of , respectively. We refer the reader to Taylor [8] for the definition of στ() and σ′′(), A point z = (z1,..., zn) of Cn is in the joint approximate point spectrum σπ() of if there exists a sequence {xk} of unit vectors in X such that∥(Ti – zi)xk∥→0 as k → ∞ for i = 1, 2,..., n. 
Chō, Muneo. Joint spectra of operators on Banach space. Glasgow mathematical journal, Tome 28 (1986) no. 1, pp. 69-72. doi: 10.1017/S0017089500006352
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