$K$-$g$-frames in Hilbert module over locally-$C^*$-algebras
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866916265058107392 |
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| author | Eljazzar, Roumaissae Mouniane, Mohammed Rossafi, Mohamed |
| author_facet | Eljazzar, Roumaissae Mouniane, Mohammed Rossafi, Mohamed |
| contents | This paper explores the concept of $K$-$g$-frames in locally $C^*$-algebras, which are shown to be more general than $g$-frames. The authors first introduce the notion of a $g$-orthonormal basis and utilize it to define the $g$-operator, a crucial element for studying the construction of $K$-$g$-frames in locally $C^*$-algebras. The paper establishes a relationship between $g$-frames and $K$-$g$-frames and introduces the $K$-dual $g$-frame along with its properties. Finally, the authors characterize $K$-$g$-frames through two other related concepts. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_18935 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | $K$-$g$-frames in Hilbert module over locally-$C^*$-algebras Eljazzar, Roumaissae Mouniane, Mohammed Rossafi, Mohamed Operator Algebras Primary 42C15, Secondary 46L05 This paper explores the concept of $K$-$g$-frames in locally $C^*$-algebras, which are shown to be more general than $g$-frames. The authors first introduce the notion of a $g$-orthonormal basis and utilize it to define the $g$-operator, a crucial element for studying the construction of $K$-$g$-frames in locally $C^*$-algebras. The paper establishes a relationship between $g$-frames and $K$-$g$-frames and introduces the $K$-dual $g$-frame along with its properties. Finally, the authors characterize $K$-$g$-frames through two other related concepts. |
| title | $K$-$g$-frames in Hilbert module over locally-$C^*$-algebras |
| topic | Operator Algebras Primary 42C15, Secondary 46L05 |
| url | https://arxiv.org/abs/2405.18935 |