On Haagerup noncommutative quasi $H^p(\A)$ spaces
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866916265835102208 |
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| author | Bekjan, Turdebek N. |
| author_facet | Bekjan, Turdebek N. |
| contents | Let $\mathcal{M}$ be a $σ$-finite von Neumann algebra, equipped with a normal faithful state $φ$, and let $\mathcal{A}$ be a maximal subdiagonal subalgebra of $\mathcal{M}$.
We have proved that for $0< p<1$, $H^p(\mathcal{A})$ is independent of $φ$. Furthermore, in the case that $\mathcal{A}$ is a type 1 subdiagonal subalgebra, we have extended the most recent results about the Riesz type factorization to the case $0<p<1$ and have proved an interpolation theorem for $H^p(\mathcal{A})$ in the case where $0 < p_0, p_1 \le \infty$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_19739 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On Haagerup noncommutative quasi $H^p(\A)$ spaces Bekjan, Turdebek N. Operator Algebras Let $\mathcal{M}$ be a $σ$-finite von Neumann algebra, equipped with a normal faithful state $φ$, and let $\mathcal{A}$ be a maximal subdiagonal subalgebra of $\mathcal{M}$. We have proved that for $0< p<1$, $H^p(\mathcal{A})$ is independent of $φ$. Furthermore, in the case that $\mathcal{A}$ is a type 1 subdiagonal subalgebra, we have extended the most recent results about the Riesz type factorization to the case $0<p<1$ and have proved an interpolation theorem for $H^p(\mathcal{A})$ in the case where $0 < p_0, p_1 \le \infty$. |
| title | On Haagerup noncommutative quasi $H^p(\A)$ spaces |
| topic | Operator Algebras |
| url | https://arxiv.org/abs/2405.19739 |