Related papers: Doubly $\Lambda$-commuting row isometries, univers…
We describe the $C_2$-equivariant homotopy type of the space of commuting n-tuples in the stable unitary group in terms of Real K-theory. The result is used to give a complete calculation of the homotopy groups of the space of commuting…
In a recent paper of the first author and Kashyap, a new class of modules over dual operator algebras is introduced. These generalize the W*-modules (that is, Hilbert C*-modules over a von Neumann algebra which satisfy an analogue of the…
We study the Wold decomposition for representations of a self-similar semigroup $P$ action on a directed graph $E$. We then apply this decomposition to the case where $P=\mathbb{N}$ to study the C*-envelope of the associated universal…
The aim of this paper is to study the Wold-type decomposition in the class of $m$-isometries. One of our main results establishes an equivalent condition for an analytic $m$-isometry to admit the Wold-type decomposition for $m\ge2$. In…
We construct classes of von Neumann algebra modules by considering ``column sums" of noncommutative L^p spaces. Our abstract characterization is based on an L^{p/2}-valued inner product, thereby generalizing Hilbert C*-modules and…
Generalising the definition to commuting $d$-tuples of operators, a number of authors have considered structural properties of $m$-isometric, $n$-symmetric and $(m,n)$-isosymmetric commuting $d$-tuples in the recent past. This note is an…
Given a row contraction of operators on Hilbert space and a family of projections on the space which stabilize the operators, we show there is a unique minimal joint dilation to a row contraction of partial isometries which satisfy natural…
A new functional model for pairs of commuting isometries is described. Intertwining operators between such models are then studied in order to approach the classification of invariant subspaces of such pairs.
Given a row-finite $k$-graph $\Lambda$ with no sources we investigate the $K$-theory of the higher rank graph $C^*$-algebra, $C^*(\Lambda)$. When $k=2$ we are able to give explicit formulae to calculate the $K$-groups of $C^*(\Lambda)$. The…
In this note, we will define the formulas of curvature and it's covariant derivatives for holomorphic curves on C*-algebras for the multivariable case. As applications, the unitarily and similarly classification theorems for holomorphic…
We associate to each unital $C^*$-algebra $A$ a geometric object---a diagram of topological spaces representing quotient spaces of the noncommutative space underlying $A$---meant to serve the role of a generalized Gel'fand spectrum. After…
We investigate C^*-algebras generated by scaling elements. We generalize the Wold decomposition and Coburn's theorem on isometries to scaling elements. We also completely determine when the C^*-algebra generated by a scaling element…
Given two C*-algebras A and B, abstract A-B bimodules that can be isometrically represented as operator bimodules are characterised in terms of their norm. Various properties of such bimodules are given. Their theory is very similar to…
We consider a net of *-algebras, locally around any point of observation, equipped with a natural partial order related to the isotony property. Assuming the underlying manifold of the net to be a differentiable, this net shall be…
We discuss basic topological properties of unitary dual spaces of nilpotent Lie groups, using some ideas from operator algebras and their noncommutative dimension theory. The general results are illustrated by many examples.
A duality theory of bundles of C$^*$-algebras whose fibres are twisted transformation group algebras is established. Classical T-duality is obtained as a special case, where all fibres are commutative tori, i.e. untwisted group algebras for…
Noncommutative lattices have been recently used as finite topological approximations in quantum physical models. As a first step in the construction of bundles and characteristic classes over such noncommutative spaces, we shall study their…
We consider the classification, up to unitary equivalence, of commuting n-tuples of isometries. We pay special attention to the case when the product of the isometries is a shift of finite multiplicity, and we provide a complete…
We develop a dilation theory for row contractions subject to constraints determined by sets of noncommutative polynomials. Under natural conditions on the constraints, we have uniqueness for the minimal dilation. A characteristic function…
We show how methods from K-theory of operator algebras can be applied in a completely algebraic setting to define a bivariant, matrix-stable, homotopy-invariant, excisive K-theory of algebras over a fixed unital ground ring H, kk_*(A,B),…