Operators taking values in Lebesgue–Bochner spaces
N Dzhusoeva, M Moslehian, M Pliev… - Proceedings of the …, 2023 - ams.org
It is a subtle fact of the theory of regular operators on Banach lattices that every linear
operator $ T\colon L_ {1}(\mu)\to L_1 (\nu) $ is norm-bounded if and only if it is regular. We …
operator $ T\colon L_ {1}(\mu)\to L_1 (\nu) $ is norm-bounded if and only if it is regular. We …
The Kalton and Rosenthal type decomposition of operators in Köthe-Bochner spaces
M Pliev, F Sukochev - Journal of Mathematical Analysis and Applications, 2021 - Elsevier
Abstract We extend the Kalton-Rosenthal representation theorem for operators on L 1 (μ) to
the setting of dominated operators on lattice-normed spaces. In the special case of Köthe …
the setting of dominated operators on lattice-normed spaces. In the special case of Köthe …
On orthogonally additive operators in Köthe–Bochner spaces
E Basaeva, R Kulaev, M Pliev - Results in Mathematics, 2021 - Springer
In this article we consider some classes of orthogonally additive operators in Köthe–Bochner
spaces in the setting of the theory of lattice-normed spaces and dominated operators. The …
spaces in the setting of the theory of lattice-normed spaces and dominated operators. The …
(Strongly-) Dunford–Pettis Operators and Narrow Operators
J Huang, M Pliev, F Sukochev - Integral Equations and Operator Theory, 2023 - Springer
Let M be a semifinite von Neumann algebra. We show that an operator T from the predual L
1 (M, τ) of M into a Banach space X is strongly Dunford–Pettis if and only if T∘ i: L 1 (M, τ)∩ …
1 (M, τ) of M into a Banach space X is strongly Dunford–Pettis if and only if T∘ i: L 1 (M, τ)∩ …