-equivalence and continuous bundles of -algebras.
-theory as the -theory of -categories.
-théorie algébrique négative et -théorie topologique de l’algèbre de Fréchet des opérateurs régularisants
-théorie bivariante de Kasparov
-theory and Toeplitz -algebras a survey
-theory for Cuntz-Krieger algebras arising from real quadratic maps.
Kernel Operators on Lp-spaces Associated with Semifinite von Neumann Algebras.
K-Groups of Toeplitz Algebras of Reinhardt Domains.
KK-theory of the full free product of unital C*-algebras.
KMS-symmetric Markov semigroups.
Kolmogoroff consistency theorem for Gleason measures
Korovkin theory in Banach -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].
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-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...
K-гомологии -алгебр