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Tensor preduals, positive homogeneity and harmonicity in two-Lipschitz spaces

  • Arindam Mandal
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Abstract

We study subspaces of two-Lipschitz mappings using group actions and tensor preduals. We first show that the ambient spaces contain large classical sequence spaces. We then use similarity actions to select smaller subspaces. Character-equivariant mappings form weak*-closed fixed-point spaces and admit quotient tensor preduals. We give two applications. For mappings on Banach spaces, we describe positive homogeneity in each variable and construct bounded projections. For mappings on finitely generated groups, we characterize harmonicity in each variable. We show that the harmonic predual is the projective tensor product of the corresponding one-variable quotient preduals.

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Cite

BibTeXRIS
BibTeX
@misc{mandal2026tensor,
  title = {{Tensor preduals, positive homogeneity and harmonicity in two-Lipschitz spaces}},
  author = {Arindam Mandal},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.04562},
  eprint = {2611.04562},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.04562},
}
RIS
TY  - UNPB
TI  - Tensor preduals, positive homogeneity and harmonicity in two-Lipschitz spaces
AU  - Arindam Mandal
PY  - 2026
DA  - 2026/11/03
PB  - arXiv
DO  - 10.48550/arxiv.2611.04562
UR  - https://arxiv.org/abs/2611.04562
AB  - We study subspaces of two-Lipschitz mappings using group actions and tensor preduals. We first show that the ambient spaces contain large classical sequence spaces. We then use similarity actions to select smaller subspaces. Character-equivariant mappings form weak^*-closed fixed-point spaces and admit quotient tensor preduals. We give two applications. For mappings on Banach spaces, we describe positive homogeneity in each variable and construct bounded projections. For mappings on finitely generated groups, we characterize harmonicity in each variable. We show that the harmonic predual is the projective tensor product of the corresponding one-variable quotient preduals.
ER  -