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- W2014392023 abstract "It is well known that the identity is an operator with the following property: if the operator, initially defined on an<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=$n$><mml:mi>n</mml:mi></mml:math>-dimensional Banach space<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=$V$><mml:mi>V</mml:mi></mml:math>, can be extended to any Banach space with norm<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=$1$><mml:mn>1</mml:mn></mml:math>, then<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=$V$><mml:mi>V</mml:mi></mml:math>is isometric to<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=$ell^{(n)}_infty$><mml:mrow><mml:msubsup><mml:mi>ℓ</mml:mi><mml:mi>∞</mml:mi><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mi>n</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:msubsup></mml:mrow></mml:math>. We show that the set of all such operators consists precisely of those with spectrum lying in the unit circle. This result answers a question raised in [5] for complex spaces." @default.
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- W2014392023 date "1998-01-01" @default.
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- W2014392023 title "Spectral properties of operators that characterizeℓ∞(n)" @default.
- W2014392023 doi "https://doi.org/10.1155/s1085337598000542" @default.
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