Related papers: A characterization of rationality for operators in…
We examine the ranks of operators in semi-finite C*-algebras as measured by their densely defined lower semicontinuous traces. We first prove that a unital simple C*-algebra whose extreme tracial boundary is nonempty and finite contains…
Let A be a unital simple separable C*-algebra with strict comparison of positive elements. We prove that the Cuntz semigroup of A is recovered functorially from the Murray-von Neumann semigroup and the tracial state space T(A) whenever the…
Let G be a group, let U(G) denote the set of unbounded operators on L^2(G) which are affiliated to the group von Neumann algebra W(G) of G, and let D(G) denote the division closure of CG in U(G). Thus D(G) is the smallest subring of U(G)…
Composition operators with analytic symbols on some reproducing kernel Hilbert spaces of entire functions on a complex Hilbert space are studied. The questions of their boundedness, seminormality and positivity are investigated. It is…
Every countable directed graph generates a Fock space Hilbert space and a family of partial isometries. These operators also arise from the left regular representations of free semigroupoids derived from directed graphs. We develop a…
We construct a Fock space associated to a symmetric function $Q:U\times U \to (-1,1)$, where $U$ is a nonempty open subset of $\mathbb R^j$ for some $j$. Namely, we will have operator-valued distributions $a(x)$ and $a^+(y)$ satisfying…
We extend the symbol calculus and study the limit operator theory for $\sigma$-compact, \'{e}tale and amenable groupoids, in the Hilbert space case. This approach not only unifies various existing results which include the cases of exact…
We show that for C*-algebras with the Global Glimm Property, the rank of every operator can be realized as the rank of a soft operator, that is, an element whose hereditary sub-C*-algebra has no nonzero, unital quotients. This implies that…
For an element in an algebra-valued *-noncommutative probability space, equivalent conditions for algebra-valued R-diagonality (a notion introduced by Sniady and Speicher) are proved. Formal power series relations involving the moments and…
We show that any $L^2$-bounded rational function in free semicircular random variables is a bounded operator, which implies the coincidence of the usual spectrum and $L^2$-spectrum for rational functions. Based on this observation, we also…
Our main result is a theorem saying that a bounded operator $A$ on a Hilbert space belongs to a certain set associated with its self-commutator $[A^*,A]$, provided that $A-zI$ can be approximated by invertible operators for all complex…
The extension problem asks whether positive semi-definite functions on a symmetric unital subset of a discrete group can be extended to positive semi-definite functions on the whole group. It has been known at least since the work of Rudin…
We study matrices whose entries are free or exchangeable noncommutative elements in some tracial $W^*$-probability space. More precisely, we consider operator-valued Wigner and Wishart matrices and prove quantitative convergence to…
Although in general there is no meaningful concept of factorization in fields, that in free associative algebras (over a commutative field) can be extended to their respective free field (universal field of fractions) on the level of…
We show a Gottlieb element in the rational homotopy of a simply connected space $X$ implies a structural result for the Sullivan minimal model, with different results depending on parity. In the even-degree case, we prove a rational…
For an arbitrary rational polyhedron we consider its decompositions into Minkowski summands and, dual to this, the free extensions of the associated pair of semigroups. Being free for the pair of semigroups is equivalent to flatness for the…
We give a general definition of classical and quantum groups whose representation theory is "determined by partitions" and study their structure. This encompasses many examples of classical groups for which Schur-Weyl duality is described…
We study selflessness in the general setting of reduced free products of $C^*$-algebras. Towards this end, we develop a suitable theory of rapid decay for filtrations in arbitrary $C^*$-probability spaces. We provide several natural…
Iteration semirings are Conway semirings satisfying Conway's group identities. We show that the semirings $\N^{\rat}\llangle \Sigma^* \rrangle$ of rational power series with coefficients in the semiring $\N$ of natural numbers are the free…
In this note we quantize the free $ * $-algebra generated by finitely many variables, which is a new example of the theory of Toeplitz quantization of $ * $-algebras as developed previously by the author. This is achieved by defining…