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Embeddings of C(K) spaces into C(S,X) spaces with distortion strictly less than 3

Leandro Candido, Elói Medina Galego (2013)

Fundamenta Mathematicae

In the spirit of the classical Banach-Stone theorem, we prove that if K and S are intervals of ordinals and X is a Banach space having non-trivial cotype, then the existence of an isomorphism T from C(K, X) onto C(S,X) with distortion | | T | | | | T - 1 | | strictly less than 3 implies that some finite topological sum of K is homeomorphic to some finite topological sum of S. Moreover, if Xⁿ contains no subspace isomorphic to X n + 1 for every n ∈ ℕ, then K is homeomorphic to S. In other words, we obtain a vector-valued Banach-Stone...

Embeddings of concave functions and duals of Lorentz spaces.

Gord Sinnamon (2002)

Publicacions Matemàtiques

A simple expression is presented that is equivalent to the norm of the Lpv → Lqu embedding of the cone of quasi-concave functions in the case 0 < q < p < ∞. The result is extended to more general cones and the case q = 1 is used to prove a reduction principle which shows that questions of boundedness of operators on these cones may be reduced to the boundedness of related operators on whole spaces. An equivalent norm for the dual of the Lorentz spaceΓp(v) = { f: ( ∫0∞ (f**)pv...

Embeddings of doubling weighted Besov spaces

Dorothee D. Haroske, Philipp Skandera (2014)

Banach Center Publications

We study continuous embeddings of Besov spaces of type B p , q s ( ℝ ⁿ , w ) , where s ∈ ℝ, 0 < p < ∞, 0 < q ≤ ∞, and the weight w is doubling. This approach generalises recent results about embeddings of Muckenhoupt weighted Besov spaces. Our main argument relies on appropriate atomic decomposition techniques of such weighted spaces; here we benefit from earlier results by Bownik. In addition, we discuss some other related weight classes briefly and compare corresponding results.

Embeddings of finite-dimensional operator spaces into the second dual

Alvaro Arias, Timur Oikhberg (2007)

Studia Mathematica

We show that, if a a finite-dimensional operator space E is such that X contains E C-completely isomorphically whenever X** contains E completely isometrically, then E is 2 15 C 11 -completely isomorphic to Rₘ ⊕ Cₙ for some n, m ∈ ℕ ∪ 0. The converse is also true: if X** contains Rₘ ⊕ Cₙ λ-completely isomorphically, then X contains Rₘ ⊕ Cₙ (2λ + ε)-completely isomorphically for any ε > 0.

Empathy theory and the Laplace transform

Niko Sauer (1997)

Banach Center Publications

This paper is concerned with double families of evolution operators employed in the study of dynamical systems in which cause and effect are represented in different Banach spaces. The main tool is the Laplace transform of vector-valued functions. It is used to define the generator of the double family which is a pair of unbounded linear operators and relates to implicit evolution equations in a direct manner. The characterization of generators for a special class of evolutions is presented.

Endomorphisms of the Cuntz algebras

Roberto Conti, Jeong Hee Hong, Wojciech Szymański (2011)

Banach Center Publications

This mainly expository article is devoted to recent advances in the study of dynamical aspects of the Cuntz algebras 𝓞ₙ, n < ∞, via their automorphisms and, more generally, endomorphisms. A combinatorial description of permutative automorphisms of 𝓞ₙ in terms of labelled, rooted trees is presented. This in turn gives rise to an algebraic characterization of the restricted Weyl group of 𝓞ₙ. It is shown how this group is related to certain classical dynamical systems on the Cantor set. An identification...

Endpoint bounds for convolution operators with singular measures

E. Ferreyra, T. Godoy, M. Urciuolo (1998)

Colloquium Mathematicae

Let S ⊂ ℝ n + 1 be the graph of the function ϕ : [ - 1 , 1 ] n → ℝ defined by ϕ ( x 1 , ⋯ , x n ) = ∑ j = 1 n | x j | β j , with 1< β 1 ≤ ⋯ ≤ β n , and let μ the measure on ℝ n + 1 induced by the Euclidean area measure on S. In this paper we characterize the set of pairs (p,q) such that the convolution operator with μ is L p - L q bounded.

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