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Bogdan Udrea

Publications and source records attributed to Bogdan Udrea.

8 recordsLinked to original sources
arXiv2023

Partially Positive Semidefinite Maps on $*$-Semigroupoids and Linearisations

Motivated by Cuntz-Krieger-Toeplitz systems associated to undirected graphs and representations of groupoids, we obtain a generalisation of the Sz-Nagy's Dilation Theorem for operator valued partially positive semidefinite maps on $*$-semigroupoids with unit, with varying degrees of aggregation, firstly by $*$-representations with unbounded operators and then we characterise the existence of the corresponding $*$-representations by bounded operators. By linearisation of these constructions, we obtain similar results for operator valued partially positive semidefinite maps on $*$-algebroids with unit and then, for the special case of $B^*$-algebroids with unit, we obtain a generalisation of the Stinespring's Dilation Theorem. As an application of the generalisation of the Stinespring's Dilation Theorem, we show that some natural questions on $C^*$-algebroids are equivalent.

math.OA↗
arXiv2018

Generalized $q$-Gaussian von Neumann algebras with coefficients, I. Relative strong solidity

We define $Γ_q(B,S \otimes H)$, the generalized $q$-gaussian von Neumann algebras associated to a sequence of symmetric independent copies $(π_j,B,A,D)$ and to a subset $1 \in S = S^* \subset A$ and, under certain assumptions, prove their strong solidity relative to $B$. We provide many examples of strongly solid generalized $q$-gaussian von Neumann algebras. We also obtain non-isomorphism and non-embedability results about some of these von Neumann algebras.

math.OA↗
arXiv2014

Some classification results for generalized q-gaussian algebras

To any trace preserving action $σ: G \curvearrowright A$ of a countable discrete group on a finite von Neumann algebra $A$ and any orthogonal representation $π:G \to \mathcal O(\ell^2_{\mathbb{R}}(G))$, we associate the generalized q-gaussian von Neumann algebra $A \rtimes_σ Γ_q^π(G,K)$, where $K$ is an infinite dimensional separable Hilbert space. Specializing to the cases of $π$ being trivial or given by conjugation, we then prove that if $G \curvearrowright A = L^{\infty}(X)$, $G' \curvearrowright B = L^{\infty}(Y)$ are p.m.p. free ergodic rigid actions, the commutator subgroups $[G,G]$, $[G',G']$ are ICC, and $G, G'$ belong to a fairly large class of groups (including all non-amenable groups having the Haagerup property), then $A \rtimes Γ_q(G,K) = B \rtimes Γ_q(G',K')$ implies that $\mathcal R(G \curvearrowright A)$ is stably isomorphic to $\mathcal R(G' \curvearrowright B)$, where $\mathcal R(G \curvearrowright A), \mathcal R(G' \curvearrowright B)$ are the countable, p.m.p. equivalence relations implemented by the actions of $G$ and $G'$ on $A$ and $B$, respectively. Using results of D. Gaboriau and S. Popa we construct continuously many pair-wise non-isomorphic von Neumann algebras of the form $L^{\infty}(X) \rtimes Γ_q(\mathbb{F}_n,K)$, for suitable free ergodic rigid p.m.p. actions $\mathbb{F}_n \curvearrowright X$.

math.OA↗
arXiv2013

On the structural theory of II_1 factors of negatively curved groups, II: Actions by product groups

This paper includes a series of structural results for von Neumann algebras arising from measure preserving actions by product groups on probability spaces. Expanding upon the methods used earlier by the first two authors \cite{CS}, we obtain new examples of strongly solid factors as well as von Neumann algebras with unique or no Cartan subalgebra. For instance we show that every II$_1$ factor associated with a weakly amenable group in the class $\mathcal S$ of Ozawa is strongly solid, \cite{OzSolid}. There is also the following product version of this result: any maximal abelian $\star$-subalgebra of any II$_1$ factor associated with a finite product of weakly amenable groups in the class $\mathcal S$ of Ozawa has an amenable normalizing algebra. Finally, pairing some of these results with cocycle superrigidity results from \cite{IoaCSR}, it follows that compact actions by finite products of lattices in $Sp(n, 1)$, $n \geq2$, are virtually $W^*$-superrigid.

math.OA↗
arXiv2013

Inner amenability for groups and central sequences in factors

We show that a large class of i.c.c., countable, discrete groups satisfying a weak negative curvature condition are not inner amenable. By recent work of Hull and Osin, our result recovers that mapping class groups and Out(F_n) are not inner amenable. We also show that the group-measure space constructions associated to free, strongly ergodic p.m.p. actions of such groups do not have property Gamma of Murray and von Neumann.

math.OA↗
arXiv2013

Aerodynamic Stability of Satellites in Elliptic Low Earth Orbits

Topical observations of the thermosphere at altitudes below $200 \, km$ are of great benefit in advancing the understanding of the global distribution of mass, composition, and dynamical responses to geomagnetic forcing, and momentum transfer via waves. The perceived risks associated with such low altitude and short duration orbits has prohibited the launch of Discovery-class missions. Miniaturization of instruments such as mass spectrometers and advances in the nano-satellite technology, associated with relatively low cost of nano-satellite manufacturing and operation, open an avenue for performing low altitude missions. The time dependent coefficients of a second order non-homogeneous ODE which describes the motion have a double periodic shape. Hence, they will be approximated using Jacobi elliptic functions. Through a change of variables the original ODE will be converted into Hill's ODE for stability analysis using Floquet theory. We are interested in how changes in the coefficients of the ODE affect the stability of the solution. The expected result will be an allowable range of parameters for which the motion is dynamically stable. A possible extension of the application is a computational tool for the rapid evaluation of the stability of entry or re-entry vehicles in rarefied flow regimes and of satellites flying in relatively low orbits.

physics.geo-ph↗