Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2512.05640 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866912751418343424 |
|---|---|
| author | Mandal, Arindam |
| author_facet | Mandal, Arindam |
| contents | In this article, we establish the existence of a norm-one projection from the space of all \emph{two-Lipschitz} operators onto the space of all bounded bilinear operators under certain conditions on the corresponding codomain spaces, using the method of invariant means. We also show that, when the codomain is an injective Banach space, the quotient of the \emph{two-Lipschitz} operator space by the bounded bilinear space is isometrically isomorphic to a specific operator space, via vector-valued duality. We conclude by proving a necessary and sufficient condition for a \emph{two-Lipschitz} operator to be a bilinear map. As an application of the theory developed here, we present an alternative proof that $\bigslant{L^{\infty}(\mathbb{R}\times \mathbb{R})}{span\{\textbf{1}\}}$ is a dual space. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_05640 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Projection from space of \emph{two-Lipschitz} operators onto the space of Bilinear maps Mandal, Arindam Functional Analysis Primary 46B28, Secondary 46B10 In this article, we establish the existence of a norm-one projection from the space of all \emph{two-Lipschitz} operators onto the space of all bounded bilinear operators under certain conditions on the corresponding codomain spaces, using the method of invariant means. We also show that, when the codomain is an injective Banach space, the quotient of the \emph{two-Lipschitz} operator space by the bounded bilinear space is isometrically isomorphic to a specific operator space, via vector-valued duality. We conclude by proving a necessary and sufficient condition for a \emph{two-Lipschitz} operator to be a bilinear map. As an application of the theory developed here, we present an alternative proof that $\bigslant{L^{\infty}(\mathbb{R}\times \mathbb{R})}{span\{\textbf{1}\}}$ is a dual space. |
| title | Projection from space of \emph{two-Lipschitz} operators onto the space of Bilinear maps |
| topic | Functional Analysis Primary 46B28, Secondary 46B10 |
| url | https://arxiv.org/abs/2512.05640 |