9 citations · 39 across the 19 of their papers we have counts for
24 papers
On amenable Hilbert-Schmidt stable groups
Caleb Eckhardt, Tatiana Shulman
We examine Hilbert-Schmidt stability (HS-stability) of discrete amenable groups from several angles. We give a short, elementary proof that finitely generated nilpotent groups are…
Commutativity of central sequence algebras
Dominic Enders, Tatiana Shulman
The question of which separable C*-algebras have abelian central sequence algebras was raised and studied by Phillips ([Ph88]) and Ando-Kirchberg ([AK14]). In this paper we give a…
Central amalgamation of groups and the RFD property
Tatiana Shulman
It is an old and challenging topic to investigate for which discrete groups G the full group C*-algebra C*(G) is residually finite-dimensional (RFD). In particular not much is know…
Almost commuting matrices, cohomology, and dimension
Dominic Enders, Tatiana Shulman
We investigate which relations for families of commuting matrices are stable under small perturbations, or in other words, which commutative -algebras are matricially s…
Free products with amalgamation over central C*-subalgebras
Kristin Courtney, Tatiana Shulman
Let A and B be C*-algebras whose quotients are all RFD, and let C be a central C*-subalgebra in both A and B. We prove that the full amalgamated free product of A and B over C is t…
C*-stability of discrete groups
Søren Eilers, Tatiana Shulman, Adam P. W. Sørensen
A group may be considered -stable if almost representations of the group in a -algebra are always close to actual representations. We initiate a systematic study of which…
Geometry of quantum dynamics in infinite dimension
Janusz Grabowski, Marek Kus, Giuseppe Marmo +1
We develop a geometric approach to quantum mechanics based on the concept of the Tulczyjew triple. Our approach is genuinely infinite-dimensional and including a Lagrangian formali…
Variations of projectivity for C*-algebras
Don Hadwin, Tatiana Shulman
We consider various lifting problems for C*-algebras. As an application of our results we show that any commuting family of order zero maps from matrices to a von Neumann central s…
Elements of -algebras Attaining Their Norm in a Finite-Dimensional Representation
Kristin Courtney, Tatiana Shulman
We characterize the class of RFD -algebras as those containing a dense subset of elements that attain their norm under a finite-dimensional representation. We show further tha…
Continuity of spectral radius and type I -algebras
Tatiana Shulman
It is shown that the spectral radius is continuous on a -algebra if and only if the -algebra is type I. This answers a question of V. Shulman and Yu.~Turovskii [10]. It i…
Stability of group relations under small Hilbert-Schmidt perturbations
Don Hadwin, Tatiana Shulman
If matrices almost satisfying a group relation are close to matrices exactly satisfying the relation, then we say that a group is matricially stable. Here "almost" and "close" are…
Tracial stability for C*-algebras
Don Hadwin, Tatiana Shulman
We consider tracial stability, which requires that tuples of elements of a C*-algebra with a trace that nearly satisfy the relation are close to tuples that actually satisfy the re…
On subspaces of invariant vectors
Tatiana Shulman
Let be the subspace of fixed vectors for a uniformly bounded representation of a group on a Banach space . We study the problem of the existence and uniqueness of…
On superactivation of one-shot zero-error quantum capacity and the related property of quantum measurements
M. E. Shirokov, Tatiana Shulman
We begin with a detailed description of a low dimensional quantum channel () demonstrating the symmetric form of superactivation of one-shot zero-error quantum capaci…
Approximations of subhomogeneous algebras
Tatiana Shulman, Otgonbayar Uuye
Let be a natural number. Recall that a C*-algebra is said to be -subhomogeneous if all its irreducible representations have dimension at most . In this short note, we giv…
Lifting algebraic contractions in C*-algebras
Terry Loring, Tatiana Shulman
Let p be a polynomial in one variable. It is shown that the universal C*-algebra of the relation p(x)=0, \|x\| \le C is semiprojective, residually finite-dimensional and has trivia…
Noncommutative Semialgebraic Sets in Nilpotent Variables
Terry A. Loring, Tatiana Shulman
We solve the lifting problem in C^*-algebras for many sets of relations that include the relations x_j^{N_j} = 0 on each variable. The remaining relations must be of the form \| p(…
A Generalized Spectral Radius Formula and Olsen's Question
Terry Loring, Tatiana Shulman
Let be a -algebra and be a closed ideal in . For , its image under the canonical surjection is denoted by , and the spectral radius of $x…
Noncommutative Semialgebraic sets and Associated Lifting Problems
Terry A. Loring, Tatiana Shulman
We solve a class of lifting problems involving approximate polynomial relations (soft polynomial relations). Various associated C*-algebras are therefore projective. The technical…
Semiprojectivity of universal C*-algebras generated by algebraic elements
Tatiana Shulman
Let be a polynomial in one variable whose roots either all have multiplicity more than 1 or all have multiplicity exactly 1. It is shown that the universal -algebra of a r…
On algebras generated by inner derivations
Tatiana Shulman, Victor Shulman
We look for an effective description of the algebra D_{Lie}(X,B) of operators on a bimodule X over an algebra B, generated by inner derivations. It is shown that in some important…
Lifting of nilpotent contractions
Tatiana Shulman
It is proved that that every nilpotent contraction in a quotient C*-algebra can be lifted to a nilpotent contraction. As a consequence we get that the universal C*-algebra generate…
On universal C^*-algebras generated by n projections with scalar sum
Tatiana Shulman
We study the universal C^*-algebras generated by n projections subject to the relation , . The questions of when these C^*-algebr…
The C*-algebras qA\otimes K and S^2A\otimes K are asymptotically equivalent
Tatiana Shulman
Let be a separable -algebra. We prove that its stabilized second suspension and the -algebra constructed by Cuntz in t…