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Passage of property \((gw)\) from two operators to their tensor product. (English) Zbl 1373.47017
Summary: A Banach space operator satisfies property \((gw)\) if the complement of its B-Weyl essential approximate point spectrum in its approximate point spectrum is the set of isolated eigenvalues of the operator. We give necessary and/or sufficient conditions ensuring the passage of property \((gw)\) from two Banach space operators \(A\) and \(B\) to their tensor product. In particular, we present a revised version of Theorem 2.3 in [M. H. M. Rashid, Ukr. Math. J. 64, No. 9, 1464–1474 (2013); translation from Ukr. Mat. Zh. 64, No. 9, 1289–1296 (2012; Zbl 1288.47020)].
MSC:
47A80 Tensor products of linear operators
47A53 (Semi-) Fredholm operators; index theories
47A10 Spectrum, resolvent
47A11 Local spectral properties of linear operators
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