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(I)-envelopes of unit balls and James' characterization of reflexivity

Ondřej F. K. Kalenda (2007)

Studia Mathematica

We study the (I)-envelopes of the unit balls of Banach spaces. We show, in particular, that any nonreflexive space can be renormed in such a way that the (I)-envelope of the unit ball is not the whole bidual unit ball. Further, we give a simpler proof of James' characterization of reflexivity in the nonseparable case. We also study the spaces in which the (I)-envelope of the unit ball adds nothing.

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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