Korovkin theory in liminal JB-algebras.
Korovkin theory in normed algebras
If A is a normed power-associative complex algebra such that the selfadjoint part is normally ordered with respect to some order, then the Korovkin closure (see the introduction for definitions) of T ∪ {t* ∘ t| t ∈ T} contains J*(T) for any subset T of A. This can be applied to C*-algebras, minimal norm ideals on a Hilbert space, and to H*-algebras. For bounded H*-algebras and dual C*-algebras there is even equality. This answers a question posed in [1].
Korovkinhüllen in Funktionenräumen.
Korovkin-type theorems and applications
Let {T n} be a sequence of linear operators on C[0,1], satisfying that {T n (e i)} converge in C[0,1] (not necessarily to e i) for i = 0,1,2, where e i = t i. We prove Korovkin-type theorem and give quantitative results on C 2[0,1] and C[0,1] for such sequences. Furthermore, we define King’s type q-Bernstein operator and give quantitative results for the approximation properties of such operators.
Köthe-Toeplitz Duals of some new Sequence Spaces and Their Matrix Maps
Krasnoselskii-type fixed point theorems under weak topology settings and applications.
Krasnosel'skii-type fixed-set results.
Kreǐn's trace formula and the spectral shift function.
Krengel-Lin decomposition for noncompact groups
K-theory of Boutet de Monvel's algebra
We consider the norm closure 𝔄 of the algebra of all operators of order and class zero in Boutet de Monvel's calculus on a compact manifold X with boundary ∂X. Assuming that all connected components of X have nonempty boundary, we show that K₁(𝔄) ≃ K₁(C(X)) ⊕ ker χ, where χ: K₀(C₀(T*Ẋ)) → ℤ is the topological index, T*Ẋ denoting the cotangent bundle of the interior. Also K₀(𝔄) is topologically determined. In case ∂X has torsion free K-theory, we get K₀(𝔄) ≃ K₀(C(X)) ⊕ K₁(C₀(T*Ẋ)).
-partitions of unity on normed spaces
-boundedness and -compactness of a class of Fourier integral operators.
Estimates for Oscillatory Integrals
estimates for pseudodifferential operators
-error analysis for a system of quasivariational inequalities with noncoercive operators.
-spaces between which all the operators are compact. I.
-spaces between which all the operators are compact. II.
-Khintchine-Bonami inequality in free probability
We prove the norm estimates for operator-valued functions on free groups supported on the words with fixed length (). Next, we replace the translations by the free generators with a free family of operators and prove inequalities of the same type.
-analyticity of Schrödinger semigroups on Riemannian manifolds
-boundedness for pseudodifferential operators with non-smooth symbols and applications
Starting from a general formulation of the characterization by dyadic crowns of Sobolev spaces, the authors give a result of continuity for pseudodifferential operators whose symbol a(x,ξ) is non smooth with respect to x and whose derivatives with respect to ξ have a decay of order ρ with . The algebra property for some classes of weighted Sobolev spaces is proved and an application to multi - quasi - elliptic semilinear equations is given.