Joint spectra of operators on Banach space
- 1 January 1986
- journal article
- research article
- Published by Cambridge University Press (CUP) in Glasgow Mathematical Journal
- Vol. 28 (1) , 69-72
- https://doi.org/10.1017/s0017089500006352
Abstract
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.Keywords
This publication has 2 references indexed in Scilit:
- Semi-Inner-Product SpacesTransactions of the American Mathematical Society, 1961
- Uniformly Convex SpacesTransactions of the American Mathematical Society, 1936