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Weyl numbers versus Z-Weyl numbers

Bernd Carl, Andreas Defant, Doris Planer (2014)

Studia Mathematica

Given an infinite-dimensional Banach space Z (substituting the Hilbert space ℓ₂), the s-number sequence of Z-Weyl numbers is generated by the approximation numbers according to the pattern of the classical Weyl numbers. We compare Weyl numbers with Z-Weyl numbers-a problem originally posed by A. Pietsch. We recover a result of Hinrichs and the first author showing that the Weyl numbers are in a sense minimal. This emphasizes the outstanding role of Weyl numbers within the theory of eigenvalue distribution...

Wheeling around von Neumann-Jordan constant in Banach spaces

J. Alonso, P. Martín, P. L. Papini (2008)

Studia Mathematica

In recent times, many constants in Banach spaces have been defined and/or studied. Relations and inequalities among them (sometimes very complicated) have been indicated. But not much effort has been devoted to organize all connections, also because the literature on the subject is growing at an always bigger rate. Here we give some new connections which better the insight on some of them. In particular, we improve a known inequality between the von Neumann-Jordan and James constants.

ρ-Orthogonality and its preservation - revisited

Jacek Chmieliński, Paweł Wójcik (2013)

Banach Center Publications

The aim of the paper is to present results concerning the ρ-orthogonality and its preservation (both accurate and approximate) by linear operators. We survey on the results presented in [11] and [23], as well as give some new and more general ones.

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