K$-$g$-frames in Hilbert module over locally-$C^$-algebras
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 $K$-$g$-fra...
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Zusammenfassung: | 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. |
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DOI: | 10.48550/arxiv.2405.18935 |