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<p>In this article, we establish the existence of a norm-one projection from the space of all <i>two-Lipschitz</i> operators onto the space of all bounded bilinear operators under certain conditions on the corresponding codomain spaces, using the method of invariant means. We also show that, when the codomain is an injective Banach space, the quotient of the <i>two-Lipschitz</i> operator space by the bounded bilinear space is isometrically isomorphic to a specific operator space, via vector-valued duality. We conclude by proving a necessary and sufficient condition for a <i>two-Lipschitz</i> operator to be a bilinear map. As an application of the theory developed here, we present an alternative proof that <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="MediaObjects/9_2026_3071_IEq1_HTML.gif" Format="GIF" Height="35" Rendition="HTML" Resolution="120" Type="Linedraw" Width="157" /> </InlineMediaObject> </InlineEquation> is a dual space.</p>

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Projection from Space of Two-Lipschitz Operators onto the Space of Bilinear Maps

  • 期刊论文

  • 发表日期：

    2026年3月2日

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  • Arindam Mandal

摘要

In this article, we establish the existence of a norm-one projection from the space of all two-Lipschitz operators onto the space of all bounded bilinear operators under certain conditions on the corresponding codomain spaces, using the method of invariant means. We also show that, when the codomain is an injective Banach space, the quotient of the two-Lipschitz operator space by the bounded bilinear space is isometrically isomorphic to a specific operator space, via vector-valued duality. We conclude by proving a necessary and sufficient condition for a two-Lipschitz operator to be a bilinear map. As an application of the theory developed here, we present an alternative proof that is a dual space.