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<p>In this paper, <i>K</i>-pseudoframes and <i>K</i>-duals for closed submodules of a Hilbert <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(C^{*}\)</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mi>C</mi> <mrow /> <mrow> <mrow /> <mo>∗</mo> </mrow> </mmultiscripts> </math></EquationSource> </InlineEquation>-module are introduced and characterized. The emphasis is on orthogonally complemented submodules and some results are also obtained for topologically complemented ones. The new concepts are related to some important notions in the theory of Hilbert <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(C^{*}\)</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mi>C</mi> <mrow /> <mrow> <mrow /> <mo>∗</mo> </mrow> </mmultiscripts> </math></EquationSource> </InlineEquation>-modules, such as morphisms, projections, orthogonal projections, and pseudo-inverses, to show their desirable behavior and present some of their useful properties.</p>

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K-duals and K-pseudoframes for closed submodules of a Hilbert \(C^*\)-module

  • 期刊论文

  • 发表日期：

    2025年12月26日

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  • Morteza Mirzaee Azandaryani,
  • Fatemeh Zamani Mirarkoulaei

摘要

In this paper, K-pseudoframes and K-duals for closed submodules of a Hilbert \(C^{*}\) C ∗ -module are introduced and characterized. The emphasis is on orthogonally complemented submodules and some results are also obtained for topologically complemented ones. The new concepts are related to some important notions in the theory of Hilbert \(C^{*}\) C ∗ -modules, such as morphisms, projections, orthogonal projections, and pseudo-inverses, to show their desirable behavior and present some of their useful properties.