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math.FA2025
Lower Bounds for the Shadiness Constant of Finite-Dimensional Normed Spaces
Jeremias Epperlein
By the Hahn-Banach theorem, every normed space admits rank-one projections with operator norm one. However, this is not true for higher rank projections. Bosznay and Garay showed t…
math.DS2025
Auerbach bases, projection constants, and the joint spectral radius of principal submatrices
Jeremias Epperlein, Fabian Wirth
It is shown that compact sets of complex matrices can always be brought, via similarity transformation, into a form where all matrix entries are bounded in absolute value by the jo…