Banach spaces which are nearly uniformly convex

Huff, Robert

doi:10.1216/rmj-1980-10-4-743

Cited by 169 publications

(119 citation statements)

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“…We refer the reader to [16] and the references therein for a detailed study of these properties. The related notions of nearly uniformly convex space (NUC for short) and nearly uniformly smooth (NUS for short) were introduced by Huff [15] and Prus [22]. A space is NUS if and only if it is AUS and reflexive and if and only if its dual is NUC.…”

Section: Introduction and Notationmentioning

confidence: 99%

On strong asymptotic uniform smoothness and convexity

García-Lirola

Raja

2017

Rev Mat Complut

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Abstract. We introduce the notions of strong asymptotic uniform smoothness and convexity. We show that the injective tensor product of strongly asymptotically uniformly smooth spaces is asymptotically uniformly smooth. This applies in particular to uniformly smooth spaces admitting a monotone FDD, extending a result by Dilworth, Kutzarova, Randrianarivony, Revalski and Zhivkov [9]. Our techniques also provide a characterisation of Orlicz functions M, N such that the space of compact operators K(h M , h N ) is asymptotically uniformly smooth. Finally we show that K(X, Y ) is not strictly convex whenever X and Y are at least two-dimensional, which extends a result by Dilworth and Kutzarova [7].

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Section: Introduction and Notationmentioning

confidence: 99%

On strong asymptotic uniform smoothness and convexity

García-Lirola

Raja

2017

Rev Mat Complut

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“…Moreover, some authors use the terms Radon-Riesz property or property (H) instead of the Kadec-Klee property (see [24]). In our terminology we follow Huff [51] who also introduced the uniform Kadec-Klee property and nearly uniform convexity. It should be noticed that independently of Huff a property equivalent to NUC was introduced in [46] under the name of noncompact uniform convexity.…”

Section: Obviously τ Cs(x) = Inf Limmentioning

confidence: 99%

Geometrical Background of Metric Fixed Point Theory

Prus

2001

Handbook of Metric Fixed Point Theory

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“…A Banach space E is said to have the uniformly Kadec-Klee (=U KK) property if for any > 0 there is a 0 < δ < 1 such that whenever (x n ) is a sequence in the unit ball of E converging weakly to x and inf{ x n − x m : n = m} > , then x ≤ δ (see Huff [12]). As is known [8], if E has the U KK property, then E has weak-normal structure and hence the fpp.…”

Section: Preliminariesmentioning

confidence: 99%

Fixed point property and normal structure for Banach spaces associated to locally compact groups

Lau

Mah

Ülger

1997

Proc. Amer. Math. Soc.

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Abstract. In this paper we investigate when various Banach spaces associated to a locally compact group G have the fixed point property for nonexpansive mappings or normal structure. We give sufficient conditions and some necessary conditions about G for the Fourier and Fourier-Stieltjes algebras to have the fixed point property. We also show that if a C * -algebra A has the fixed point property then for any normal element a of A, the spectrum σ(a) is countable and that the group C * -algebra C * (G) has weak normal structure if and only if G is finite.

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Banach spaces which are nearly uniformly convex

Cited by 169 publications

References 0 publications

On strong asymptotic uniform smoothness and convexity

On strong asymptotic uniform smoothness and convexity

Geometrical Background of Metric Fixed Point Theory

Fixed point property and normal structure for Banach spaces associated to locally compact groups

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