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Coefficient of orthogonal convexity of some Banach function spaces

Paweł Kolwicz, Stefan Rolewicz (2004)

Studia Mathematica

We study orthogonal uniform convexity, a geometric property connected with property (β) of Rolewicz, P-convexity of Kottman, and the fixed point property (see [19, [20]). We consider the coefficient of orthogonal convexity in Köthe spaces and Köthe-Bochner spaces.

Coincidence of topologies on tensor products of Köthe echelon spaces

J. Bonet, A. Defant, A. Peris, M. Ramanujan (1994)

Studia Mathematica

We investigate conditions under which the projective and the injective topologies coincide on the tensor product of two Köthe echelon or coechelon spaces. A major tool in the proof is the characterization of the επ-continuity of the tensor product of two diagonal operators from l p to l q . Several sharp forms of this result are also included.

Combinatorial inequalities and subspaces of L₁

Joscha Prochno, Carsten Schütt (2012)

Studia Mathematica

Let M₁ and M₂ be N-functions. We establish some combinatorial inequalities and show that the product spaces ℓ ⁿ M ₁ ( ℓ ⁿ M ₂ ) are uniformly isomorphic to subspaces of L₁ if M₁ and M₂ are “separated” by a function t r , 1 < r < 2.

Commutative, radical amenable Banach algebras

C. Read (2000)

Studia Mathematica

There has been a considerable search for radical, amenable Banach algebras. Noncommutative examples were finally found by Volker Runde [R]; here we present the first commutative examples. Centrally placed within the construction, the reader may be pleased to notice a reprise of the undergraduate argument that shows that a normed space with totally bounded unit ball is finite-dimensional; we use the same idea (approximate the norm 1 vector x within distance η by a “good” vector y 1 ; then approximate...

Commutators on ( ∑ ℓ q ) p

Dongyang Chen, William B. Johnson, Bentuo Zheng (2011)

Studia Mathematica

Let T be a bounded linear operator on X = ( ∑ ℓ q ) p with 1 ≤ q < ∞ and 1 < p < ∞. Then T is a commutator if and only if for all non-zero λ ∈ ℂ, the operator T - λI is not X-strictly singular.

Compact embeddings of Brézis-Wainger type.

Fernando Cobos, Thomas Kühn, Tomas Schonbek (2006)

Revista Matemática Iberoamericana

Let Ω be a bounded domain in Rn and denote by idΩ the restriction operator from the Besov space Bpq1+n/p(Rn) into the generalized Lipschitz space Lip(1,-α)(Ω). We study the sequence of entropy numbers of this operator and prove that, up to logarithmic factors, it behaves asymptotically like ek(idΩ) ~ k-1/p if α &gt; max (1 + 2/p + 1/q, 1/p). Our estimates improve previous results by Edmunds and Haroske.

Compact operators between K- and J-spaces

Fernando Cobos, Luz M. Fernández-Cabrera, Antón Martínez (2005)

Studia Mathematica

The paper establishes necessary and sufficient conditions for compactness of operators acting between general K-spaces, general J-spaces and operators acting from a J-space into a K-space. Applications to interpolation of compact operators are also given.

Compact operators whose adjoints factor through subspaces of l p

Deba P. Sinha, Anil K. Karn (2002)

Studia Mathematica

For p ≥ 1, a subset K of a Banach space X is said to be relatively p-compact if K ⊂ ∑ n = 1 ∞ α ₙ x ₙ : α ₙ ∈ B a l l ( l p ' ) , where p’ = p/(p-1) and x ₙ ∈ l p s ( X ) . An operator T ∈ B(X,Y) is said to be p-compact if T(Ball(X)) is relatively p-compact in Y. Similarly, weak p-compactness may be defined by considering x ₙ ∈ l p w ( X ) . It is proved that T is (weakly) p-compact if and only if T* factors through a subspace of l p in a particular manner. The normed operator ideals ( K p , κ p ) of p-compact operators and ( W p , ω p ) of weakly p-compact operators, arising from these factorizations,...

Compact spaces that do not map onto finite products

Antonio Avilés (2009)

Fundamenta Mathematicae

We provide examples of nonseparable compact spaces with the property that any continuous image which is homeomorphic to a finite product of spaces has a maximal prescribed number of nonseparable factors.

Currently displaying 61 – 80 of 203