Geodesic
Passage of Property $(aw)$ from Two Operators to their Tensor Product
Kragujevac Journal of Mathematics, Tome 42 (2018) no. 3, p. 389 .

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A Banach space operator $S$ satisfies property $(aw)$ if $\s(S)\setminus\sw(S)=E_a^0(S)$, where $E_a^0(S)$ is the set of all isolated point in the approximate point spectrum which are eigenvalues of finite multiplicity. Property $(aw)$ does not transfer from operators $A$ and $B$ to their tensor product $A\otimes B$, so we give necessary and/or sufficient conditions ensuring the passage of property $(aw)$ from $A$ and $B$ to $A\otimes B$. Perturbations by Riesz operators are considered.
Classification : 47A53, 47B20 47A10, 47A11
Keywords: tensor product, property $(aw)$, perturbation, SVEP 
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     author = {M. H. M. Rashid},
     title = {Passage of {Property} $(aw)$ from {Two} {Operators} to their {Tensor} {Product}},
     journal = {Kragujevac Journal of Mathematics},
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     publisher = {mathdoc},
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     number = {3},
     year = {2018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KJM_2018_42_3_a5/}
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M. H. M. Rashid. Passage of Property $(aw)$ from Two Operators to their Tensor Product. Kragujevac Journal of Mathematics, Tome 42 (2018) no. 3, p. 389 . http://geodesic.mathdoc.fr/item/KJM_2018_42_3_a5/