Research output: Contribution to journal › Article › peer-review
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.Research output: Contribution to journal › Article › peer-review
}
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