Composition operators on Musielak-Orlicz spaces of Bochner type
The invertible, closed range, compact, Fredholm and isometric composition operators on Musielak-Orlicz spaces of Bochner type are characterized in the paper.
Composition operators on the Bergman space
Composition operators on the Dirichlet space and related problems.
Composition operators on vector-valued Hardy spaces.
Composition operators on W 1 X are necessarily induced by quasiconformal mappings
Let Ω ⊂ ℝn be an open set and X(Ω) be any rearrangement invariant function space close to L q(Ω), i.e. X has the q-scaling property. We prove that each homeomorphism f which induces the composition operator u ↦ u ℴ f from W 1 X to W 1 X is necessarily a q-quasiconformal mapping. We also give some new results for the sufficiency of this condition for the composition operator.
Composition results for strongly summing and dominated multilinear operators
In this paper we prove some composition results for strongly summing and dominated operators. As an application we give necessary and sufficient conditions for a multilinear tensor product of multilinear operators to be strongly summing or dominated. Moreover, we show the failure of some possible n-linear versions of Grothendieck’s composition theorem in the case n ≥ 2 and give a new example of a 1-dominated, hence strongly 1-summing bilinear operator which is not weakly compact.
Compositions of operator ideals and their regular hulls
Compositions of operators with vector valued maps
Compound invariants and embeddings of Cartesian products
New compound geometric invariants are constructed in order to characterize complemented embeddings of Cartesian products of power series spaces. Bessaga's conjecture is proved for the same class of spaces.
Compressible groups
Compressible operators and the continuity of homomorphisms from algebras of operators
The notion of a compressible operator on a Banach space, E, derives from automatic continuity arguments. It is related to the notion of a cartesian Banach space. The compressible operators on E form an ideal in ℬ(E) and the automatic continuity proofs depend on showing that this ideal is large. In particular, it is shown that each weakly compact operator on the James' space, J, is compressible, whence it follows that all homomorphisms from ℬ(J) are continuous.
Computation of some examples of Brown's spectral measure in free probability
We use free probability techniques to compute spectra and Brown measures of some non-hermitian operators in finite von Neumann algebras. Examples include where uₙ and are the generators of ℤₙ and ℤ respectively, in the free product ℤₙ*ℤ, or elliptic elements of the form where and are free semicircular elements of variance α and β.
Computing and estimating the global dimension in certain classes af Banach algebras.
Computing discrete convolutions with verified accuracy via Banach algebras and the FFT
We introduce a method to compute rigorous component-wise enclosures of discrete convolutions using the fast Fourier transform, the properties of Banach algebras, and interval arithmetic. The purpose of this new approach is to improve the implementation and the applicability of computer-assisted proofs performed in weighed Banach algebras of Fourier/Chebyshev sequences, whose norms are known to be numerically unstable. We introduce some application examples, in particular a rigorous aposteriori...
Computing norms and critical exponents of some operators in -spaces
Computing summing norms and type constants on few vectors
Concentration inequalities for s-concave measures of dilations of Borel sets and applications.
Concentration of mass on the Schatten classes
Concentration of measure and logarithmic Sobolev inequalities
Concentration-Compactness Principle for embedding into multiple exponential spaces on unbounded domains
Let be a domain and let . We prove the Concentration-Compactness Principle for the embedding of the space into an Orlicz space corresponding to a Young function which behaves like for large . We also give the result for the embedding into multiple exponential spaces. Our main result is Theorem where we show that if one passes to unbounded domains, then, after the usual modification of the integrand in the Moser functional, the statement of the Concentration-Compactnes Principle is very...