Research output: Contribution to journal › Article › peer-review
On factorization of operators through the spaces lp. / Reinov, O. I.
In: Vestnik Sankt-Peterburgskogo Universiteta. Ser 1. Matematika Mekhanika Astronomiya, No. 2, 2000, p. 27-32.Research output: Contribution to journal › Article › peer-review
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TY - JOUR
T1 - On factorization of operators through the spaces lp
AU - Reinov, O. I.
N1 - Copyright: Copyright 2004 Elsevier Science B.V., Amsterdam. All rights reserved.
PY - 2000
Y1 - 2000
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=0034587784&partnerID=8YFLogxK
M3 - статья
AN - SCOPUS:0034587784
SP - 27
EP - 32
JO - ВЕСТНИК САНКТ-ПЕТЕРБУРГСКОГО УНИВЕРСИТЕТА. МАТЕМАТИКА. МЕХАНИКА. АСТРОНОМИЯ
JF - ВЕСТНИК САНКТ-ПЕТЕРБУРГСКОГО УНИВЕРСИТЕТА. МАТЕМАТИКА. МЕХАНИКА. АСТРОНОМИЯ
SN - 1025-3106
IS - 2
ER -
ID: 73500330