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Subjects
46-XX Functional analysis
46Bxx Normed linear spaces and Banach spaces; Banach lattices
46B45 Banach sequence spaces

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Geometry of modulus spaces.

Khalil, R., Hussein, D., Amin, W. (2002)

Georgian Mathematical Journal

Geometry of Orlicz spaces [Book]

Chen Shutao (1996)

Geometry of quotient spaces and proximinality

Yuan Cui, Henryk Hudzik, Yaowaluck Khongtham (2003)

Annales Polonici Mathematici

It is proved that if X is a rotund Banach space and M is a closed and proximinal subspace of X, then the quotient space X/M is also rotund. It is also shown that if Φ does not satisfy the δ₂-condition, then $h ⁰_{Φ}$ is not proximinal in $l ⁰_{Φ}$ and the quotient space $l ⁰_{Φ} / h ⁰_{Φ}$ is not rotund (even if $l ⁰_{Φ}$ is rotund). Weakly nearly uniform convexity and weakly uniform Kadec-Klee property are introduced and it is proved that a Banach space X is weakly nearly uniformly convex if and only if it is reflexive and it has the weakly...

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