Korovkin theory in Banach -algebras
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.
Köthe coechelon spaces as locally convex algebras
We study those Köthe coechelon sequence spaces , 1 ≤ p ≤ ∞ or p = 0, which are locally convex (Riesz) algebras for pointwise multiplication. We characterize in terms of the matrix V = (vₙ)ₙ when an algebra is unital, locally m-convex, a -algebra, has a continuous (quasi)-inverse, all entire functions act on it or some transcendental entire functions act on it. It is proved that all multiplicative functionals are continuous and a precise description of all regular and all degenerate maximal ideals...
Köthe dual of Banach sequence spaces and Grothendieck space
In this paper, we show the representation of Köthe dual of Banach sequence spaces
Köthe spaces modeled on spaces of functions
The isomorphic classification problem for the Köthe models of some function spaces is considered. By making use of some interpolative neighborhoods which are related to the linear topological invariant and other invariants related to the “quantity” characteristics of the space, a necessary condition for the isomorphism of two such spaces is proved. As applications, it is shown that some pairs of spaces which have the same interpolation property are not isomorphic.
Köthe-Toeplitz Duals of some new Sequence Spaces and Their Matrix Maps
Krein-space operators determined by free product algebras induced by primes and graphs
In this paper, we introduce certain Krein-space operators induced by free product algebras induced by both primes and directed graphs. We study operator-theoretic properties of such operators by computing free-probabilistic data containing number-theoretic data.
K-theoretic amenability for discrete groups.
K-theory from the point of view of C*-algebras and Fredholm representations
These notes represent the subject of five lectures which were delivered as a minicourse during the VI conference in Krynica, Poland, “Geometry and Topology of Manifolds”, May, 2–8, 2004.
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)).
K-theory over C*-algebras
The contents of the article represents the minicourse which was delivered at the 7th conference "Geometry and Topology of Manifolds. The Mathematical Legacy of Charles Ehresmann", Będlewo (Poland), 8.05.2005 - 15.05.2005. The article includes the description of the so called Hirzebruch formula in different aspects which lead to a basic list of problems related to noncommutative geometry and topology. In conclusion, two new problems are presented: about almost flat bundles and about the Noether decomposition...
Kuttner's theorem for operators
Kvaziasimptotičeskoe razloženie meri (Quasiasymptotic decomposition of measures).
K-гомологии -алгебр