Proof of the Paszkiewicz's conjecture about a product of positive contractions
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866910478895153152 |
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| author | Ando, Hiroshi Miyamoto, Yuki Ozawa, Narutaka |
| author_facet | Ando, Hiroshi Miyamoto, Yuki Ozawa, Narutaka |
| contents | The Paszkiewicz conjecture about a product of positive contractions asserts that given a decreasing sequence $T_1\ge T_2\ge \dots$ of positive contractions on a separable infinite-dimensional Hilbert space, the product $S_n=T_n\dots T_1$ converges strongly. Recently, the first named author verified the conjecture for certain classes of sequences. In this paper, we prove the Paszkiewicz conjecture in full generality. Moreover, we show that in some cases, a generalized version of the Paszkiewicz conjecture also holds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_10770 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Proof of the Paszkiewicz's conjecture about a product of positive contractions Ando, Hiroshi Miyamoto, Yuki Ozawa, Narutaka Functional Analysis Operator Algebras Spectral Theory 47A63, 47A65 The Paszkiewicz conjecture about a product of positive contractions asserts that given a decreasing sequence $T_1\ge T_2\ge \dots$ of positive contractions on a separable infinite-dimensional Hilbert space, the product $S_n=T_n\dots T_1$ converges strongly. Recently, the first named author verified the conjecture for certain classes of sequences. In this paper, we prove the Paszkiewicz conjecture in full generality. Moreover, we show that in some cases, a generalized version of the Paszkiewicz conjecture also holds. |
| title | Proof of the Paszkiewicz's conjecture about a product of positive contractions |
| topic | Functional Analysis Operator Algebras Spectral Theory 47A63, 47A65 |
| url | https://arxiv.org/abs/2405.10770 |