Zachary spaces $\mathcal{Z}^p[\mathbb{R}^{\infty }]$ and separable Banach spaces

Hemanata Kalita; Bipan Hazarika; Mohsen Rabbani

Zachary spaces $\mathcal{Z}^p[\mathbb{R}^{\infty }]$ and separable Banach spaces

Functional Analysis 2022-06-09 v2

Authors: Hemanata Kalita , Bipan Hazarika , Mohsen Rabbani

Abstract

We construct Zachary space in $\R^\infty$ and find that this is a Banach space of functions of bounded mean oscillation with order $p, 1\leq p \leq \infty$ containing the function of bounded mean oscillation $BMO[\R_I^\infty]$ as a dense continuous embedding. As an application of $\R_I^\infty$ we construction $\mcB,$ where $\mcB$ is separable Banach space and finally we construct $\mcZ^p[\mcB]$ .

Keywords

banach spaces bmo spaces

Cite

@article{arxiv.2010.13627,
  title  = {Zachary spaces $\mathcal{Z}^p[\mathbb{R}^{\infty }]$ and separable Banach spaces},
  author = {Hemanata Kalita and Bipan Hazarika and Mohsen Rabbani},
  journal= {arXiv preprint arXiv:2010.13627},
  year   = {2022}
}

Comments

12 pages. Constructive comments expected from expert of this area. arXiv admin note: text overlap with arXiv:2002.11512

Zachary spaces $\mathcal{Z}^p[\mathbb{R}^{\infty }]$ and separable Banach spaces

Abstract

Keywords

Cite

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