Unless we say otherwise, every vector space we talk about is taken to be over C. A Banach algebra is a Banach space A that is also an algebra satisfying ‖AB‖ ≤ ‖A‖ ‖B‖ for A,B ∈ A. We say that A is unital if there is a nonzero element I ∈ A such that AI = A and IA = A for all A ∈ A, called a identity element. If X is a Banach space, let B(X) denote the set of bounded linear operators X → X, and...

Let A, B be separable simple unital tracially AF C*-algebras. Assuming that A is exact and satisfies the Universal Coefficient Theorem (UCT) in KK-theory, we prove the existence, and uniqueness modulo approximately inner automorphisms, of nuclear ∗-homomorphisms from A to B with prescribed K-theory data. This implies the AF-embeddability of separable exact residually finite dimensional C*-algeb...

Working under large cardinal assumptions, we study the Borel-reducibility between equivalence relations modulo restrictions of the non-stationary ideal on some fixed cardinal κ. We show the consistency of E ++,λ++ λ-club , the relation of equivalence modulo the non-stationary ideal restricted to Sλ ++ λ in the space (λ++)λ ++ , being continuously reducible to E ++ λ+-club , the relation of equi...

We study self-homeomorphisms of zero dimensional metrizable compact Hausdorff spaces by means of the ordered first cohomology group, particularly in the light of the recent work of Giordano, Putnam, and Skau on minimal homeomorphisms. We show that flow equivalence of systems is analogous to Morita equivalence between algebras, and this is reflected in the ordered cohomology group. We show that ...

Let $A$ be the quotient of a graded polynomial ring $\mathbb{Z}[x_1,\cdots,x_m]\otimes\Lambda[y_1,\cdots,y_n]$ by an ideal generated monomials with leading coefficients 1. Then we constructed space~$X_A$ such that is isomorphic to $H^*(X_A)$ modulo torsion elements.

It is proved that the cone of a separable nuclearly embeddable residually finite-dimensional C*-algebra embeds in the CAR algebra (the UHF algebra of type 2∞). As a corollary we obtain a short new proof of Kirchberg’s theorem asserting that a separable unital C*-algebra A is nuclearly embeddable if and only there is a semisplit extension 0 → J → E → A → 0 with E a unital C*-subalgebra of the CA...

Let φ be a linear-fractional self-map of the open unit disk D, not an automorphism, such that φ(ζ) = η for two distinct points ζ, η in the unit circle ∂D. We consider the question of which composition operators lie in C∗(Cφ,K), the unital C∗-algebra generated by the composition operator Cφ and the ideal K of compact operators, acting on the Hardy space H. This necessitates a companion study of ...

We consider extensions of unital commutative rings. We define an extension R ↪→ S to be a p-extension if every principally generated ideal of S is generated by an element of R. Examples are plentiful and localizations of regular multiplicative sets are p-extensions. We develop the theory of pextensions.

We consider extensions of unital commutative rings. We define an extension R ↪→ S to be a p-extension if every principally generated ideal of S is generated by an element of R. Examples are plentiful and localizations of regular multiplicative sets are p-extensions. We develop the theory of pextensions.