On Extensions of Bilinear Maps

DOI10.1515/MS-2022-0066arXiv2110.03102MaRDI QIDQ6379616

C. S. Kubrusly

Publication date: 6 October 2021

Abstract: The paper deals with extension of bounded bilinear maps$.$ It gives a necessary and sufficient condition for extending a bounded bilinear map on the Cartesian product of subspaces of Banach spaces$.$ This leads to a full characterization for extension of bounded bilinear maps on the Cartesian product of arbitrary subspaces of Hilbert spaces$.$ Applications concerning projective tensor products are also investigated.

Mathematics Subject Classification ID

Theorems of Hahn-Banach type; extension and lifting of functionals and operators (46A22) Extension of maps (54C20) Tensor products in functional analysis (46M05) Forms (bilinear, sesquilinear, multilinear) (47A07)

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