Estimating Norms of Commutators

Loring, Terry A.; Vides, Fredy

doi:10.1080/10586458.2014.958355

Cited by 4 publications

(2 citation statements)

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“…Some generalizations of T.4.2 and particular applications of L.4.5 to the study of matrix equations on words will also be the subject of future study. In particular, the combination of toroidal matrix links with some matrix lifting techniques along the same lines of the proof of T.4.2 combined with L.4.5, seem also promising on the solvability of some conjectures studied numerically on [28].…”

Section: Hints and Future Directionsmentioning

confidence: 99%

Local matrix homotopies and soft tori

Loring¹,

Vides²

2018

Banach J. Math. Anal.

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Abstract. We present solutions to local connectivity problems in matrix representations of the form C([−1, 1] N ) → An,ε ← Cε(T 2 ) for any ε ∈ [0, 2] and any integer n ≥ 1, where An,ε ⊆ Mn and where Cε(T 2 ) denotes the Soft Torus. We solve the connectivity problems by introducing the so called toroidal matrix links, which can be interpreted as normal contractive matrix analogies of free homotopies in differential algebraic topology.In order to deal with the locality constraints, we have combined some techniques introduced in this document with some techniques from matrix geometry, combinatorial optimization, classification and representation theory of C * -algebras.

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Section: Hints and Future Directionsmentioning

confidence: 99%

Local matrix homotopies and soft tori

Loring¹,

Vides²

2018

Banach J. Math. Anal.

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“…We need a special case of a lemma in [18]. Before we focus on our choice of the three functions f , g and h to use in the Bott invariant, we look at the terms we need to control when bounding B(U, V ) 2 − I.…”

Section: Proof That the Gap Persistsmentioning

confidence: 99%

Quantitative K-Theory Related to Spin Chern Numbers

Loring¹

2014

SIGMA

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Abstract. 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, that of general unitary matrices and that of self-dual matrices, with an emphasis on quantitative results. We determine which values of the norm of the commutator guarantee that the indices are defined, where they are equal, and what quantitative results on the distance to a pair with a different index are possible. We validate a method of computing spin Chern numbers that was developed with Hastings and only conjectured to be correct. Specifically, the Pfaffian-Bott index can be computed by the "log method" for commutator norms up to a specific constant.

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AbstractC⁎-Algebras

2018

C*-Algebras and Their Automorphism Groups

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Estimating Norms of Commutators

Abstract: We discuss a general method of finding bounds on the norm of a commutator of an operator and a function of a normal operator. As an application we find new bounds on the norm of a commuator with a square root.

Cited by 4 publications

References 12 publications

Local matrix homotopies and soft tori

Local matrix homotopies and soft tori

Quantitative K-Theory Related to Spin Chern Numbers

AbstractC⁎-Algebras

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