Differences of idempotents in \(C^\ast\)-algebras and the quantum Hall effect

DOI10.1134/S0040577918040074zbMath1401.81091OpenAlexW2801181749MaRDI QIDQ1794529

Airat M. Bikchentaev

Publication date: 15 October 2018

Published in: Theoretical and Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s0040577918040074

zbMATH Keywords

symmetrytrace-class operatorHilbert spaceidempotenttraceprojectionlinear operatorquantum Hall effectunitary operator\(C^\ast\)-algebra

Mathematics Subject Classification ID

Linear operators belonging to operator ideals (nuclear, (p)-summing, in the Schatten-von Neumann classes, etc.) (47B10) Applications of selfadjoint operator algebras to physics (46L60) Many-body theory; quantum Hall effect (81V70)

Related Items

Universal decomposition equalities for operator matrices in a Hilbert space ⋮ Trace and commutators of measurable operators affiliated to a von Neumann algebra ⋮ Unnamed Item ⋮ Differences and commutators of idempotents in \(C^*\)-algebras ⋮ On \(\tau \)-essentially invertibility of \(\tau \)-measurable operators ⋮ Studies on noncommutative measure theory in Kazan university (1968--2018) ⋮ Characterization of tracial functionals on von Neumann algebras ⋮ Rearrangements of tripotents and differences of isometries in semifinite von Neumann algebras ⋮ Projections and traces on von Neumann algebras ⋮ Trace inequalities for Rickart \(C^{\ast}\)-algebras ⋮ Trace and differences of idempotents in \(C^\ast\)-algebras ⋮ Tripotents in algebras: ideals and commutators ⋮ Characterization of certain traces on von Neumann algebras ⋮ Differences and commutators of projections on a Hilbert space

Cites Work

• Unnamed Item
• On idempotent \(\tau\)-measurable operators affiliated to a von Neumann algebra
• Commutativity of projections and characterization of traces on von Neumann algebras
• Representation of tripotents and representations via tripotents
• Commutation of projections and trace characterization on von Neumann algebras. II.
• Commutation of projections and characterization of traces on von Neumann algebras. III
• On a property of \(L_p\) spaces on semifinite von Neumann algebras
• The index of a pair of projections
• A note on pairs of projections
• Fredholm properties of the difference of orthogonal projections in a Hilbert space
• The difference and sum of projectors
• Tripotents in algebras: invertibility and hyponormality
• Differences of idempotents in \(C^\ast\)-algebras
• From Mathematical Physics to Analysis: A Walk in Barry Simon's Mathematical Garden, II
• The noncommutative geometry of the quantum Hall effect
• Invertibility of the Difference of Idempotents