<p>Let <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="9_2025_2892_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="17" /> </InlineMediaObject> <EquationSource Format="TEX">\(A\)</EquationSource> <EquationSource Format="MATHML"><math> <mi>A</mi> </math></EquationSource> </InlineEquation> be a complex Banach space with a norm <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="9_2025_2892_Article_IEq2.gif" Format="GIF" Height="20" Rendition="HTML" Resolution="72" Type="Linedraw" Width="168" /> </InlineMediaObject> <EquationSource Format="TEX">\(\left\| f\right\| =\left\| f\right\| _{X}+\left\| d(f)\right\| _{Y}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mfenced close="∥" open="∥"> <mi>f</mi> </mfenced> <mo>=</mo> <msub> <mfenced close="∥" open="∥"> <mi>f</mi> </mfenced> <mi>X</mi> </msub> <mo>+</mo> <msub> <mfenced close="∥" open="∥"> <mi>d</mi> <mo stretchy="false">(</mo> <mi>f</mi> <mo stretchy="false">)</mo> </mfenced> <mi>Y</mi> </msub> </mrow> </math></EquationSource> </InlineEquation> for <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="9_2025_2892_Article_IEq3.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="49" /> </InlineMediaObject> <EquationSource Format="TEX">\(f\in A\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>f</mi> <mo>∈</mo> <mi>A</mi> </mrow> </math></EquationSource> </InlineEquation>, where <i>d</i> is a complex linear map from <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="9_2025_2892_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="17" /> </InlineMediaObject> <EquationSource Format="TEX">\(A\)</EquationSource> <EquationSource Format="MATHML"><math> <mi>A</mi> </math></EquationSource> </InlineEquation> onto a Banach space <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="9_2025_2892_Article_IEq5.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="17" /> </InlineMediaObject> <EquationSource Format="TEX">\(B\)</EquationSource> <EquationSource Format="MATHML"><math> <mi>B</mi> </math></EquationSource> </InlineEquation>, and <InlineEquation ID="IEq6"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="9_2025_2892_Article_IEq6.gif" Format="GIF" Height="20" Rendition="HTML" Resolution="72" Type="Linedraw" Width="37" /> </InlineMediaObject> <EquationSource Format="TEX">\(\left\| \cdot \right\| _{K}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mfenced close="∥" open="∥"> <mo>·</mo> </mfenced> <mi>K</mi> </msub> </math></EquationSource> </InlineEquation> represents the supremum norm on a compact Hausdorff space <InlineEquation ID="IEq7"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="9_2025_2892_Article_IEq7.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="19" /> </InlineMediaObject> <EquationSource Format="TEX">\(K\)</EquationSource> <EquationSource Format="MATHML"><math> <mi>K</mi> </math></EquationSource> </InlineEquation>. In this paper, we characterize surjective isometries on <InlineEquation ID="IEq8"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="9_2025_2892_Article_IEq8.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="56" /> </InlineMediaObject> <EquationSource Format="TEX">\((A,\left\| \cdot \right\| )\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <mi>A</mi> <mo>,</mo> <mfenced close="∥" open="∥"> <mo>·</mo> </mfenced> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>, which may be nonlinear. This unifies former results on surjective isometries between specific function spaces.</p>