Extreme points in quotients of Hardy spaces
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866918419099549696 |
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| author | Dyakonov, Konstantin M. |
| author_facet | Dyakonov, Konstantin M. |
| contents | In the Hardy spaces $H^1$ and $H^\infty$, there are neat and well-known characterizations of the extreme points of the unit ball. We obtain counterparts of these classical theorems when $H^1$ (resp., $H^\infty$) gets replaced by the quotient space $H^1/E$ (resp., $H^\infty/E$), under certain assumptions on the subspace $E$. In the $H^1$ setting, we also treat the case where the underlying space is taken to be the kernel of a Toeplitz operator. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_29103 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Extreme points in quotients of Hardy spaces Dyakonov, Konstantin M. Functional Analysis Classical Analysis and ODEs Complex Variables 30H05, 30H10, 30J05, 46A55, 47B35 In the Hardy spaces $H^1$ and $H^\infty$, there are neat and well-known characterizations of the extreme points of the unit ball. We obtain counterparts of these classical theorems when $H^1$ (resp., $H^\infty$) gets replaced by the quotient space $H^1/E$ (resp., $H^\infty/E$), under certain assumptions on the subspace $E$. In the $H^1$ setting, we also treat the case where the underlying space is taken to be the kernel of a Toeplitz operator. |
| title | Extreme points in quotients of Hardy spaces |
| topic | Functional Analysis Classical Analysis and ODEs Complex Variables 30H05, 30H10, 30J05, 46A55, 47B35 |
| url | https://arxiv.org/abs/2603.29103 |