Related papers: Julia operators and Halmos dilations

This is the first in a series of papers where we study logarithmic intertwining operators for various vertex subalgebras of Heisenberg vertex operator algebras. In this paper we examine logarithmic intertwining operators associated with…

Given a densely defined and closed operator $A$ acting on a complex Hilbert space $\mathcal{H}$, we establish a one-to-one correspondence between its closed extensions and subspaces $\mathfrak{M}\subset\mathcal{D}(A^*)$, that are closed…

Given an essential ideal $J\subset A$ of a C*-algebra $A$, and a Hilbert C*-module $M$ over $A$, we place $M$ between two other Hilbert C*-modules over $A$, $M_J\subset M\subset M^J$, in such a way that each submodule here is thick, i.e.…

Let $\mathfrak{A}$ and $\mathfrak{B}$ be JBW$^*$-algebras whose sets of unitaries are denoted by $\mathcal{U}(\mathfrak{A})$ and $\mathcal{U}(\mathfrak{B})$, respectively. We show that $\mathcal{U}(\mathfrak{A})$ is closed for Jordan…

Let $q = e^{i \theta} \in \mathbb{T}$ (where $\theta \in \mathbb{R}$), and let $u,v$ be $q$-commuting unitaries, i.e., $u$ and $v$ are unitaries such that $vu = quv$. In this paper we find the optimal constant $c = c_\theta$ such that $u,v$…

Recent results have shown that any closed operator $A$ commuting with the backwards shift $S^*$ restricted to $K ^2_u := H^2 \ominus u H^2$, where $u$ is an inner function, can be realized as a Nevanlinna function of $S^*_u := S^*…

We define a strong Morita-type equivalence $\sim _{\sigma \Delta }$ for operator algebras. We prove that $A\sim _{\sigma \Delta }B$ if and only if $A$ and $B$ are stably isomorphic. We also define a relation $\subset _{\sigma \Delta }$ for…

We show that a Hilbert space bounded linear operator has an $m$-isometric lifting for some integer $m\ge 1$ if and only if the norms of its powers grow polynomially. In analogy with unitary dilations of contractions, we prove that such…

In this note, we present a characterization of semistable unitary operators on $L^2(\mathbb{R})$, under the assumption that the operator is (i) translation-invariant, (ii) symmetric, and (iii) locally uniformly continuous (LUC) under…

Let A and B be commutative locally convex algebras with unit. A is assumed to be a uniform topological algebra. Let h be an injective homomorphism from A to B. Under additional assumptions, we characterize the continuity of the homomorphism…

We show that the convolution algebra of smooth, compactly-supported functions on a Lie groupoid is H-unital in the sense of Wodzicki. We also prove H-unitality of infinite order vanishing ideals associated to invariant, closed subsets of…

In general, it is a non trivial task to determine the adjoint $S^*$ of an unbounded operator $S$ acting between two Hilbert spaces. We provide necessary and sufficient conditions for a given operator $T$ to be identical with $S^*$. In our…

For any nonnegative self-adjoint operators A and B in a separable Hilbert space, we show that the Trotter-type formula $[(e^{i2tA/n}+e^{i2tB/n})/2]^n$ converges strongly in the closure of the intersection of the domains of A^{1/2} and…

We introduce a notion of cobordism of Callias-type operators over complete Riemannian manifolds and prove that the index is preserved by such a cobordism. As an application we prove a gluing formula for Callias-type index. In particular, a…

We consider sets of operations on a set A that are closed under permutation of variables, addition of dummy variables and composition. We describe these closed sets in terms of a Galois connection between operations and systems of pointed…

We consider contractive homomorphisms of a planar algebra ${\mathcal A}(\Omega)$ over a finitely connected bounded domain $\Omega \subseteq \C$ and ask if they are necessarily completely contractive. We show that a homomorphism…

We consider contractive operators $T$ that are trace class perturbations of a unitary operator $U$. We prove that the dimension functions of the absolutely continuous spectrum of $T$, $T^*$ and of $U$ coincide. In particular, if $U$ has a…

In this note, we provide a family of $2\times 2$ tetrablock contractions that have tetrablock isometric dilation, but the corresponding fundamental operators do not commute. This answers a question raised by Bhattacharyya [Indiana Univ.…

A general construction is given for a class of invertible maps between the classical $U(sl(2))$ and the Jordanian $U_{h}(sl(2))$ algebras. Different maps are directly useful in different contexts. Similarity trasformations connecting them,…

This paper analyzes the action {\delta} of a Lie algebra X by derivations on a C*-algebra A. This action satisfies an "almost inner" property which ensures affiliation of the generators of the derivations {\delta} with A, and is expressed…