On factorization of operators through the spaces lp › Научные исследования в СПбГУ

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On factorization of operators through the spaces l^p. / Reinov, O. I.

в: Vestnik Sankt-Peterburgskogo Universiteta. Ser 1. Matematika Mekhanika Astronomiya, № 2, 2000, стр. 27-32.

Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование

Harvard

Reinov, OI 2000, 'On factorization of operators through the spaces l^p', Vestnik Sankt-Peterburgskogo Universiteta. Ser 1. Matematika Mekhanika Astronomiya, № 2, стр. 27-32.

APA

Reinov, O. I. (2000). On factorization of operators through the spaces l^p. Vestnik Sankt-Peterburgskogo Universiteta. Ser 1. Matematika Mekhanika Astronomiya, (2), 27-32.

Vancouver

Reinov OI. On factorization of operators through the spaces l^p. Vestnik Sankt-Peterburgskogo Universiteta. Ser 1. Matematika Mekhanika Astronomiya. 2000;(2):27-32.

Author

Reinov, O. I. / On factorization of operators through the spaces l^p. в: Vestnik Sankt-Peterburgskogo Universiteta. Ser 1. Matematika Mekhanika Astronomiya. 2000 ; № 2. стр. 27-32.

BibTeX

@article{7fe94095d7d64051813370f1685bb22c,

title = "On factorization of operators through the spaces lp",

abstract = "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.",

author = "Reinov, {O. I.}",

year = "2000",

language = "русский",

pages = "27--32",

journal = "ВЕСТНИК САНКТ-ПЕТЕРБУРГСКОГО УНИВЕРСИТЕТА. МАТЕМАТИКА. МЕХАНИКА. АСТРОНОМИЯ",

issn = "1025-3106",

publisher = "Издательство Санкт-Петербургского университета",

number = "2",

}

RIS

TY - JOUR

T1 - On factorization of operators through the spaces lp

AU - Reinov, O. I.

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