Abstract
Given a finite-dimensional Banach space <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper E"> <mml:semantics> <mml:mi>E</mml:mi> <mml:annotation encoding="application/x-tex">E</mml:annotation> </mml:semantics> </mml:math> </inline-formula> and a Euclidean norm on <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper E"> <mml:semantics> <mml:mi>E</mml:mi> <mml:annotation encoding="application/x-tex">E</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, we study relations between the norm and the Euclidean norm on subspaces of <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper E"> <mml:semantics> <mml:mi>E</mml:mi> <mml:annotation encoding="application/x-tex">E</mml:annotation> </mml:semantics> </mml:math> </inline-formula> of small codimension. Then for an operator taking values in a Hilbert space, we deduce an inequality for entropy numbers of the operator and its dual.
Keywords
AlgorithmAnnotationLinear subspaceBanach spaceComputer scienceMathematicsArtificial intelligenceDiscrete mathematicsPure mathematics
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Publication Info
- Year
- 1986
- Type
- article
- Volume
- 97
- Issue
- 4
- Pages
- 637-642
- Citations
- 124
- Access
- Closed
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Cite This
Alain Pajor,
Nicole Tomczak-Jaegermann
(1986).
Subspaces of small codimension of finite-dimensional Banach spaces.
Proceedings of the American Mathematical Society
, 97
(4)
, 637-642.
https://doi.org/10.1090/s0002-9939-1986-0845980-8
Identifiers
- DOI
- 10.1090/s0002-9939-1986-0845980-8