227 citations · 968 across the 42 of their papers we have counts for
22 papers · 1 filter
Even spheres as joint spectra of matrix models
Alexander Cerjan, Terry A. Loring
The Clifford spectrum is a form of joint spectrum for noncommuting matrices. This theory has been applied in photonics, condensed matter and string theory. In applications, the Cli…
Surfaces and hypersurfaces as the joint spectrum of matrices
Patrick H. DeBonis, Terry A. Loring, Roman Sverdlov
The Clifford spectrum is an elegant way to define the joint spectrum of several Hermitian operators. While it has been know that for examples as small as three -by- matrices…
Local Matrix Homotopies and Soft Tori
Terry A. Loring, Fredy Vides
We present solutions to local connectivity problems in matrix representations of the form for any $…
K-Theory for Real C*-algebras via Unitary Elements with Symmetries
Jeffrey L. Boersema, Terry A. Loring
We prove that all eight KO groups for a real C*-algebra can be constructed from homotopy classes of unitary matrices that respect a variety of symmetries. In this manifestation of…
Almost Commuting Orthogonal Matrices
Terry A. Loring, Adam P. W. Sørensen
We show that almost commuting real orthogonal matrices are uniformly close to exactly commuting real orthogonal matrices. We prove the same for symplectic unitary matrices. This is…
Principal angles and approximation for quaternionic projections
Terry A. Loring
We extend Jordan's notion of principal angles to work for two subspaces of quaternionic space, and so have a method to analyze two orthogonal projections in M_n(A) for A the real,…
Quantitative K-Theory Related to Spin Chern Numbers
Terry A. Loring
We examine the various indices defined on pairs of almost commuting unitary matrices that can detect pairs that are far from commuting pairs. We do this in two symmetry classes, th…
Estimating Norms of Commutators
Terry A. Loring, Fredy Vides
We find estimates on the norms commutators of the form [f(x), y] in terms of the norm of [x, y] assuming that x and y are contractions in a C*-algebra A, with x normal and with spe…
Pictures of KK-theory for real C*-algebras and almost commuting matrices
Jeffrey L. Boersema, Terry A. Loring, Efren Ruiz
We give a systematic account of the various pictures of KK-theory for real C*-algebras, proving natural isomorphisms between the groups that arise from each picture. As part of thi…
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…
Almost commuting unitary matrices related to time reversal
Terry A. Loring, Adam P. W. Sørensen
The behavior of fermionic systems depends on the geometry of the system and the symmetry class of the Hamiltonian and observables. Almost commuting matrices arise from band-project…
Factorization of Matrices of Quaternions
Terry A. Loring
We review known factorization results in quaternion matrices. Specifically, we derive the Jordan canonical form, polar decomposition, singular value decomposition, the QR factoriza…
The Point in Weak Semiprojectivity and AANR Compacta
Terry A. Loring
We initiate the study of pointed approximative absolute neighborhood retracts. Our motivation is to generate examples of C*-algebras that behave in unexpected ways with respect to…
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(…
Almost commuting self-adjoint matrices --- the real and self-dual cases
Terry A. Loring, Adam P. W. Sørensen
We show that a pair of almost commuting self-adjoint, symmetric matrices is close to a pair of commuting self-adjoint, symmetric matrices (in a uniform way). Moreover we prove that…
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…
Weakly Projective C*-Algebras
Terry A. Loring
The noncommutative analog of an approximative absolute retract (AAR) is introduced, a weakly projective C*-algebra. This property sits between being residually finite dimensional a…
From Matrix to Operator Inequalities
Terry A. Loring
We generalize Loewner's method for proving that matrix monotone functions are operator monotone. The relation x \leq y on bounded operators is our model for a definition for C*-rel…
C*-Algebra Relations
Terry A. Loring
We investigate relations on elements in C*-algebras, including *-polynomial relations, order relations and all relations that correspond to universal C*-algebras. We call these C*-…
Projective C*-Algebras and Boundary Maps
Terry A. Loring
Both boundary maps in K-theory are expressed in terms of surjections from projective C*-algebras to semiprojective C*-algebras.
A Projective C*-Algebra Related to K-Theory
Terry A. Loring
The C*-algebra qC is the smallest of the C*-algebras qA introduced by Cuntz in the context of KK-theory. An important property of qC is the natural isomorphism of K0 of D with clas…