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<p>The main purpose of this paper is to study the Bishop-Phelps-Bollobás property for operators on <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10476_2025_70_Article_IEq2.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="15" /> </InlineMediaObject> <EquationSource Format="TEX">\(c_0\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>c</mi> <mn>0</mn> </msub> </math></EquationSource> </InlineEquation>-sum of Euclidean spaces. We show that the pair <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10476_2025_70_Article_IEq3.gif" Format="GIF" Height="21" Rendition="HTML" Resolution="72" Type="Linedraw" Width="119" /> </InlineMediaObject> <EquationSource Format="TEX">\( (c_0(\bigoplus^{\infty}_{k=1}\ell^{k}_{2} ),Y)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <msub> <mi>c</mi> <mn>0</mn> </msub> <mrow> <mo stretchy="false">(</mo> <msubsup> <mo>⨁</mo> <mrow> <mi>k</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>∞</mi> </msubsup> <msubsup> <mi>ℓ</mi> <mn>2</mn> <mi>k</mi> </msubsup> <mo stretchy="false">)</mo> </mrow> <mo>,</mo> <mi>Y</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> has the Bishop-Phelps-Bollobás property for operators (shortly BPBp for operators) whenever <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10476_2025_70_Article_IEq4.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="14" /> </InlineMediaObject> <EquationSource Format="TEX">\(Y\)</EquationSource> <EquationSource Format="MATHML"><math> <mi>Y</mi> </math></EquationSource> </InlineEquation> is a uniformly convex Banach space.</p>

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The Bishop-Phelps-Bollobás property for operators defined on \(c_0\)-sum of Euclidean spaces

  • 期刊论文

  • 发表日期：

    2025年2月24日

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  • T. Grando,
  • M. L. Lourenço

摘要

The main purpose of this paper is to study the Bishop-Phelps-Bollobás property for operators on \(c_0\) c 0 -sum of Euclidean spaces. We show that the pair \( (c_0(\bigoplus^{\infty}_{k=1}\ell^{k}_{2} ),Y)\) ( c 0 ( ⨁ k = 1 ∞ ℓ 2 k ) , Y ) has the Bishop-Phelps-Bollobás property for operators (shortly BPBp for operators) whenever \(Y\) Y is a uniformly convex Banach space.