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On James and Jordan-von Neumann constants and the normal structure coefficient of Banach spaces

Mikio Kato, Lech Maligranda, Yasuji Takahashi (2001)

Studia Mathematica

Some relations between the James (or non-square) constant J(X) and the Jordan-von Neumann constant C N J ( X ) , and the normal structure coefficient N(X) of Banach spaces X are investigated. Relations between J(X) and J(X*) are given as an answer to a problem of Gao and Lau [16]. Connections between C N J ( X ) and J(X) are also shown. The normal structure coefficient of a Banach space is estimated by the C N J ( X ) -constant, which implies that a Banach space with C N J ( X ) -constant less than 5/4 has the fixed point property.

On Kottman's constants in Banach spaces

Jesús M. F. Castillo, Pier Luigi Papini (2011)

Banach Center Publications

This paper deals with a few, not widely known, aspects of Kottman's constant of a Banach space and its symmetric and finite variations. We will consider their behaviour under ultrapowers, relations with other parameters such as Whitley's or James' constant, and connection with the extension of c₀-valued Lipschitz maps.

On local convexity of nonlinear mappings between Banach spaces

Iryna Banakh, Taras Banakh, Anatolij Plichko, Anatoliy Prykarpatsky (2012)

Open Mathematics

We find conditions for a smooth nonlinear map f: U → V between open subsets of Hilbert or Banach spaces to be locally convex in the sense that for some c and each positive ɛ < c the image f(B ɛ(x)) of each ɛ-ball B ɛ(x) ⊂ U is convex. We give a lower bound on c via the second order Lipschitz constant Lip2(f), the Lipschitz-open constant Lipo(f) of f, and the 2-convexity number conv2(X) of the Banach space X.

On modular approximation property in the Besicovitch-Orlicz space of almost periodic functions

Mohamed Morsli (1997)

Commentationes Mathematicae Universitatis Carolinae

We investigate some convergence questions in the class of Besicovitch-Orlicz spaces of vector valued functions. Next, the existence problem of the projection operator on closed convex subsets is considered in the class of almost periodic functions. This problem was considered in [5], in the case of an Orlicz space. The approximation property obtained in both cases are of the same kind. However, the arguments which are used in the proofs are different.

On monotonic functions from the unit interval into a Banach space with uncountable sets of points of discontinuity

Artur Michalak (2003)

Studia Mathematica

We say that a function f from [0,1] to a Banach space X is increasing with respect to E ⊂ X* if x* ∘ f is increasing for every x* ∈ E. We show that if f: [0,1] → X is an increasing function with respect to a norming subset E of X* with uncountably many points of discontinuity and Q is a countable dense subset of [0,1], then (1) l i n f ( [ 0 , 1 ] ) ¯ contains an order isomorphic copy of D(0,1), (2) l i n f ( Q ) ¯ contains an isomorphic copy of C([0,1]), (3) l i n f ( [ 0 , 1 ] ) ¯ / l i n f ( Q ) ¯ contains an isomorphic copy of c₀(Γ) for some uncountable set Γ, (4) if...

On multilinear mappings attaining their norms.

Maria Acosta (1998)

Studia Mathematica

We show, for any Banach spaces X and Y, the denseness of the set of bilinear forms on X × Y whose third Arens transpose attains its norm. We also prove the denseness of the set of norm attaining multilinear mappings in the class of multilinear mappings which are weakly continuous on bounded sets, under some additional assumptions on the Banach spaces, and give several examples of classical spaces satisfying these hypotheses.

On n -normed spaces.

Gunawan, Hendra, Mashadi, M. (2001)

International Journal of Mathematics and Mathematical Sciences

On nested sequences of convex sets in Banach spaces

Jesús M. F. Castillo, Manuel González, Pier Luigi Papini (2014)

Studia Mathematica

We study different aspects of the representation of weak*-compact convex sets of the bidual X** of a separable Banach space X via a nested sequence of closed convex bounded sets of X.

Currently displaying 521 – 540 of 1093