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<p>We generalize results concerning Gel’fand integration of functions taking values in the space of operators on Hilbert spaces to certain Banach spaces. Building on ideas from [<CitationRef CitationID="CR10">10</CitationRef>] we provide sufficient conditions for the Gel’fand integral to be <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\((q,p)-\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <mi>q</mi> <mo>,</mo> <mi>p</mi> <mo stretchy="false">)</mo> <mo>-</mo> </mrow> </math></EquationSource> </InlineEquation>summing and we use the developed techniques to answer a question posed in the mentioned article. Applications to positive operator-valued functions between certain function spaces are also given.</p>

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Gel’fand Integration of \(\varvec{\mathcal {B}}(E,F^*)\)-Valued Functions With Emphasis on (q, p)-Summing Operators

  • 期刊论文

  • 发表日期：

    2026年2月4日

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  • Matija Milović,
  • Stefan Milošević

摘要

We generalize results concerning Gel’fand integration of functions taking values in the space of operators on Hilbert spaces to certain Banach spaces. Building on ideas from [10] we provide sufficient conditions for the Gel’fand integral to be \((q,p)-\) ( q , p ) - summing and we use the developed techniques to answer a question posed in the mentioned article. Applications to positive operator-valued functions between certain function spaces are also given.