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On Lindenstrauss-Pełczyński spaces

Jesús M. F. Castillo, Yolanda Moreno, Jesús Suárez (2006)

Studia Mathematica

We consider some stability aspects of the classical problem of extension of C(K)-valued operators. We introduce the class ℒ of Banach spaces of Lindenstrauss-Pełczyński type as those such that every operator from a subspace of c₀ into them can be extended to c₀. We show that all ℒ-spaces are of type ℒ ∞ but not conversely. Moreover, ℒ ∞ -spaces will be characterized as those spaces E such that E-valued operators from w*(l₁,c₀)-closed subspaces of l₁ extend to l₁. Regarding examples we will show that...

On linear extension for interpolating sequences

Eric Amar (2008)

Studia Mathematica

Let A be a uniform algebra on X and σ a probability measure on X. We define the Hardy spaces H p ( σ ) and the H p ( σ ) interpolating sequences S in the p-spectrum ℳ p of σ. We prove, under some structural hypotheses on A and σ, that if S is a “dual bounded” Carleson sequence, then S is H s ( σ ) -interpolating with a linear extension operator for s < p, provided that either p = ∞ or p ≤ 2. In the case of the unit ball of ℂⁿ we find, for instance, that if S is dual bounded in H ∞ ( ) then S is H p ( ) -interpolating with a linear...

On Lipschitz and d.c. surfaces of finite codimension in a Banach space

Luděk Zajíček (2008)

Czechoslovak Mathematical Journal

Properties of Lipschitz and d.c. surfaces of finite codimension in a Banach space and properties of generated σ -ideals are studied. These σ -ideals naturally appear in the differentiation theory and in the abstract approximation theory. Using these properties, we improve an unpublished result of M. Heisler which gives an alternative proof of a result of D. Preiss on singular points of convex functions.

On local automorphisms and mappings that preserve idempotents

Matej Brešar, Peter Šemrl (1995)

Studia Mathematica

Let B(H) be the algebra of all bounded linear operators on a Hilbert space H. Automorphisms and antiautomorphisms are the only bijective linear mappings θ of B(H) with the property that θ(P) is an idempotent whenever P ∈ B(H) is. In case H is separable and infinite-dimensional, every local automorphism of B(H) is an automorphism.

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.

Currently displaying 601 – 620 of 1948