When is a subspace of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.svg"> <mml:msubsup> <mml:mrow> <mml:mi>ℓ</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>∞</mml:mo> </mml:mrow> <mml:mrow> <mml:mi>N</mml:mi> </mml:mrow> </mml:msubsup

It is shown in this note that one can decide whether an n -dimensional subspace of ℓ ∞ N is isometrically isomorphic to ℓ ∞ n by testing a finite number of determinental inequalities. As a byproduct, an elementary proof is provided for the fact that an n -dimensional subspace of ℓ ∞ N with projection constant equal to one must be isometrically isomorphic to ℓ ∞ n .