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- Title
On Extension of Multilinear Operators and Homogeneous Polynomials in Vector Lattices.
- Authors
Kusraeva, Z. A.
- Abstract
We establish the existence of a simultaneous extension from a majorizing sublattice in the classes of regular multilinear operators and regular homogeneous polynomials on vector lattices. By simultaneous extension from a sublattice we mean a right inverse of the restriction operator to this sublattice which is an order continuous lattice homomorphism. The main theorems generalize some earlier results for orthogonally additive polynomials and bilinear operators. The proofs base on linearization by Fremlin's tensor product and the existence of a right inverse of an order continuous operator with Levy and Maharam property.
- Subjects
RIESZ spaces; HOMOGENEOUS polynomials; MULTILINEAR algebra; POLYNOMIAL operators; BANACH lattices; TENSOR products; HOMOMORPHISMS
- Publication
Siberian Mathematical Journal, 2023, Vol 64, Issue 5, p1179
- ISSN
0037-4466
- Publication type
Article
- DOI
10.1134/S0037446623050105