Quantum stochastic convolution cocycles I
Quantum stochastic dynamics on type III factors
Quantum stochastic processes arising from the strong resolvent limits of the Schrödinger evolution in Fock space
By using F. A. Berezin's canonical transformation method [5], we derive a nonadapted quantum stochastic differential equation (QSDE) as an equation for the strong limit of the family of unitary groups satisfying the Schrödinger equation with singularly degenerating Hamiltonians in Fock space. Stochastic differentials of QSDE generate a nonadapted associative Ito multiplication table, and the coefficients of these differentials satisfy the formal unitarity conditions of the Hudson-Parthasarathy type...
Quantum stopping times and quasi-left continuity
Quantum SU(2) and the Baum-Connes conjecture
We review the formulation and proof of the Baum-Connes conjecture for the dual of the quantum group of Woronowicz. As an illustration of this result we determine the K-groups of quantum automorphism groups of simple matrix algebras.
Quantum symmetries in noncommutative C*-systems
We introduce the notion of a completely quantum C*-system (A,G,α), i.e. a C*-algebra A with an action α of a compact quantum group G. Spectral properties of completely quantum systems are investigated. In particular, it is shown that G-finite elements form the dense *-subalgebra of A. Furthermore, properties of ergodic systems are studied. We prove that there exists a unique α-invariant state ω on A. Its properties are described by a family of modular operators acting on . It turns out that ω...
Quantum ultrametrics on AF algebras and the Gromov-Hausdorff propinquity
We construct quantum metric structures on unital AF algebras with a faithful tracial state, and prove that for such metrics, AF algebras are limits of their defining inductive sequences of finite-dimensional C*-algebras for the quantum propinquity. We then study the geometry, for the quantum propinquity, of three natural classes of AF algebras equipped with our quantum metrics: the UHF algebras, the Effrös-Shen AF algebras associated with continued fraction expansions of irrationals, and the Cantor...
Quarks, fractals, non-linearities, and related elliptic operators
Quasi *-algebras of measurable operators
Non-commutative -spaces are shown to constitute examples of a class of Banach quasi *-algebras called CQ*-algebras. For p ≥ 2 they are also proved to possess a sufficient family of bounded positive sesquilinear forms with certain invariance properties. CQ*-algebras of measurable operators over a finite von Neumann algebra are also constructed and it is proven that any abstract CQ*-algebra (,₀) with a sufficient family of bounded positive tracial sesquilinear forms can be represented as a CQ*-algebra...
Quasi *-algebras valued quantized fields
Quasi totally barrelled spaces
Quasi-abelian categories and sheaves
Quasianalytic vectors and derivations of operator algebras.
Quasiasymptotic expansion of distributions from and the asymptotic expansion of the distributional Stieltjes transform.
Quasiasymptotic expansion of distributions with applications to the Stieltjes transform
Quasi-Banach algebras, ideals, and holomorphic functional calculus
Quasi-Banach Spaces which are Unique Predual.
Quasibarrelled and bornological vector groups
Quasibeschränkte Fredholmoperatoren.
Quasi-bounded sets.