Research output: Contribution to journal › Article › peer-review
We give conditions on a pair of Banach spaces X and Y, under which (*) each operator from X to Y, whose second adjoined member compactly factors through the space lp, 1≤p≤+∞, itself compactly factors through lp. The conditions are as follows: either the space X*, or the space Y*** possesses the Grothendieck approximation property. Leaving the corresponding question for parameters p>1, p≠2, still open we show that for p=1 the conditions are essential: there exist Banach spaces with the bases for which the assertion (*) is invalid for the case of l1-factoring operators.
Original language | Russian |
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Pages (from-to) | 27-32 |
Number of pages | 6 |
Journal | Vestnik Sankt-Peterburgskogo Universiteta. Ser 1. Matematika Mekhanika Astronomiya |
Issue number | 2 |
State | Published - 2000 |
ID: 73500330