an:06692721
Zbl 1373.47017
Amouch, Mohamed; Zguitti, Hassane
Passage of property \((gw)\) from two operators to their tensor product
EN
Ital. J. Pure Appl. Math. 36, 283-292 (2016).
00363948
2016
j
47A80 47A53 47A10 47A11
property \((gw)\); generalized \(a\)-Weyl's theorem; tensor product
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 [\textit{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)].
Zbl 1288.47020