Geometry of quotient spaces and proximinality

• Autorzy: Yuan Cui , Henryk Hudzik , Yaowaluck Khongtham
• Języki publikacji: EN

Abstrakty

EN

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 $h⁰_{Φ}$ is not proximinal in $l⁰_{Φ}$ and the quotient space $l⁰_{Φ}/h⁰_{Φ}$ is not rotund (even if $l⁰_{Φ}$ 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 uniform Kadec-Klee property. It is noted that the quotient space X/M with X and M as above is weakly nearly uniformly convex whenever X is weakly nearly uniformly convex. Criteria for weakly nearly uniform convexity of Orlicz sequence spaces equipped with the Orlicz norm are given.

Kategorie tematyczne

• 46E40: Spaces of vector- and operator-valued functions
• 46E30: Spaces of measurable functions ( L p -spaces, Orlicz spaces, K\"othe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
• 46B20: Geometry and structure of normed linear spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 2003
• Tom: 82
• Numer: 1
• Strony: 9-18

Daty

wydano

2003

Twórcy

autor

Yuan Cui

• Department of Mathematics, Harbin University of Sciences, and Technology, Harbin, P.R. China

autor

Henryk Hudzik

• Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Umultowska 87, 61-614 Poznań, Poland

autor

Yaowaluck Khongtham

• Faculty of Science, Maejo University, Chiang Mai, Thailand

Identyfikatory

DOI

10.4064/ap82-1-2