Abstract
This is the first paper to consider the isometric extension problem of an into–mapping between the unit spheres of two different types of spaces. We prove that, under some conditions, an into–isometric mapping from the unit sphere \( S{\left( {{\ell }^{\infty }_{{{\left( 2 \right)}}} } \right)} \) to \( S{\left( {L^{1} {\left( \mu \right)}} \right)} \) can be (real) linearly isometrically extended.
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