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On the tensor products of operators in Lebesgue spaces. / Reinov, O. I.

In: Journal of Mathematical Sciences , Vol. 102, No. 5, 2000, p. 4487-4507.

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Reinov, OI 2000, 'On the tensor products of operators in Lebesgue spaces', Journal of Mathematical Sciences , vol. 102, no. 5, pp. 4487-4507. https://doi.org/10.1007/BF02672902

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Reinov, O. I. / On the tensor products of operators in Lebesgue spaces. In: Journal of Mathematical Sciences . 2000 ; Vol. 102, No. 5. pp. 4487-4507.

BibTeX

@article{53a457dd067f426fb4a72bb9d99d4868,
title = "On the tensor products of operators in Lebesgue spaces",
abstract = "The following question concerning the computation of the norms of the tensor products of operators in the Lebesgue spaces is studied: Is it true that the norm of the tensor product A ⊗ B : Lp (μ ⊗ μ) → Lq (ν ⊗ ν) of operators A : Lp(μ) → Lq(ν) and B : Lp(μ) → L q(ν) coincides with the product ∥A∥∥B∥ of their norms? An answer is positive if and only if l ≤ p ≤ q ≤ + ∞.",
author = "Reinov, {O. I.}",
note = "Funding Information: This work was partially supported by the Ministry of Education of the Russian Federation (grant No. 97-0-1.7-3.6) and the Federal Program {"}INTEGRATSIYA{"} (grant No. 326.53). Copyright: Copyright 2017 Elsevier B.V., All rights reserved.",
year = "2000",
doi = "10.1007/BF02672902",
language = "English",
volume = "102",
pages = "4487--4507",
journal = "Journal of Mathematical Sciences",
issn = "1072-3374",
publisher = "Springer Nature",
number = "5",

}

RIS

TY - JOUR

T1 - On the tensor products of operators in Lebesgue spaces

AU - Reinov, O. I.

N1 - Funding Information: This work was partially supported by the Ministry of Education of the Russian Federation (grant No. 97-0-1.7-3.6) and the Federal Program "INTEGRATSIYA" (grant No. 326.53). Copyright: Copyright 2017 Elsevier B.V., All rights reserved.

PY - 2000

Y1 - 2000

N2 - The following question concerning the computation of the norms of the tensor products of operators in the Lebesgue spaces is studied: Is it true that the norm of the tensor product A ⊗ B : Lp (μ ⊗ μ) → Lq (ν ⊗ ν) of operators A : Lp(μ) → Lq(ν) and B : Lp(μ) → L q(ν) coincides with the product ∥A∥∥B∥ of their norms? An answer is positive if and only if l ≤ p ≤ q ≤ + ∞.

AB - The following question concerning the computation of the norms of the tensor products of operators in the Lebesgue spaces is studied: Is it true that the norm of the tensor product A ⊗ B : Lp (μ ⊗ μ) → Lq (ν ⊗ ν) of operators A : Lp(μ) → Lq(ν) and B : Lp(μ) → L q(ν) coincides with the product ∥A∥∥B∥ of their norms? An answer is positive if and only if l ≤ p ≤ q ≤ + ∞.

UR - http://www.scopus.com/inward/record.url?scp=52849117374&partnerID=8YFLogxK

U2 - 10.1007/BF02672902

DO - 10.1007/BF02672902

M3 - Article

AN - SCOPUS:52849117374

VL - 102

SP - 4487

EP - 4507

JO - Journal of Mathematical Sciences

JF - Journal of Mathematical Sciences

SN - 1072-3374

IS - 5

ER -

ID: 73500166