Factorization of anti-linear and $C$-normal operators
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866913253365383168 |
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| author | Bhuia, Sudip Ranjan |
| author_facet | Bhuia, Sudip Ranjan |
| contents | A conjugation $C$ is an anti-linear isometric involution on a complex Hilbert space $\clh$, and $T\in \clb(\clh)$ is conjugate normal if $T^*T = CTT^*C$ holds for some conjugation (C). In this paper, we provide a factorization and range inclusion theorem for anti-linear operators, and consequently, establish the polar decomposition for anti-linear operators by applying the Douglas theorem on majorization of Hilbert space operators. Moreover, we present a factorization of $C$-normal operators based on the polar decomposition. Lastly, we study the Cartesian decomposition of conjugate normal operators, thereby expanding the results in [18]. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2403_02207 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Factorization of anti-linear and $C$-normal operators Bhuia, Sudip Ranjan Functional Analysis Primary 47A65, Secondary 47A68, 47B15 A conjugation $C$ is an anti-linear isometric involution on a complex Hilbert space $\clh$, and $T\in \clb(\clh)$ is conjugate normal if $T^*T = CTT^*C$ holds for some conjugation (C). In this paper, we provide a factorization and range inclusion theorem for anti-linear operators, and consequently, establish the polar decomposition for anti-linear operators by applying the Douglas theorem on majorization of Hilbert space operators. Moreover, we present a factorization of $C$-normal operators based on the polar decomposition. Lastly, we study the Cartesian decomposition of conjugate normal operators, thereby expanding the results in [18]. |
| title | Factorization of anti-linear and $C$-normal operators |
| topic | Functional Analysis Primary 47A65, Secondary 47A68, 47B15 |
| url | https://arxiv.org/abs/2403.02207 |