On the standard K-loop structure of positive invertible elements in a \(C^\ast\)-algebra

DOI10.1016/j.jmaa.2014.05.009zbMath1308.46061OpenAlexW1992660460MaRDI QIDQ2252088

Lajos Molnár, Roberto Beneduci

Publication date: 16 July 2014

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2014.05.009

zbMATH Keywords

loop\(C^\ast\)-algebraK-looppositive invertibles in a \(C^\ast\)-algebra

Mathematics Subject Classification ID

General theory of (C^*)-algebras (46L05)

Related Items (23)

The equivalence of gyrocommutative gyrogroups and K-loops ⋮ Commuting pairs of normal operators ⋮ Maps on the positive definite cone of a \(C^\ast\)-algebra preserving certain quasi-entropies ⋮ On certain order properties of non Kubo-Ando means in operator algebras ⋮ On a characterization of commutativity for {\(C^*\)}-algebras via gyrogroup operations ⋮ Characterizations of Jordan \(^*\)-isomorphisms of \(C^*\)-algebras by weighted geometric mean related operations and quantities ⋮ On local automorphisms of some quantum mechanical structures of Hilbert space operators ⋮ A Mazur-Ulam theorem for normed gyrolinear spaces ⋮ The arithmetic, geometric and harmonic means in operator algebras and transformations among them ⋮ Some new characterizations of central positive elements in \(C^\ast\)-algebras ⋮ Commuting pairs of self-adjoint elements in C ^*-algebras ⋮ A few conditions for a \(C^*\)-algebra to be commutative ⋮ On preservers related to the spectral geometric mean ⋮ Examples and applications of generalized gyrovector spaces ⋮ On a class of determinant preserving maps for finite von Neumann algebras ⋮ Piecewise \(^\ast\)-homomorphisms and Jordan maps on \(C^\ast\)-algebras and factor von Neumann algebras ⋮ Involutive groups, unique 2-divisibility, and related gyrogroup structures ⋮ Additivity of quadratic maps on JB algebras ⋮ Algebraic structures for means ⋮ On the nonexistence of order isomorphisms between the sets of all self-adjoint and all positive definite operators ⋮ Maps on Quantum States in -algebras Preserving von Neumann Entropy or Schatten -norm of Convex Combinations ⋮ The operation $ABA$ in operator algebras ⋮ A new look at local maps on algebraic structures of matrices and operators

Cites Work

• Unit balls, Lorentz boosts, and hyperbolic geometry
• Sequential product and Jordan product of quantum effects
• Sequential product of quantum effects: an overview
• Order automorphisms on positive definite operators and a few applications
• Selected preserver problems on algebraic structures of linear operators and on function spaces
• On the notion of gyrogroup
• Theory of K-loops
• Symmetric sets with midpoints and algebraically equivalent theories
• Isometries and maps compatible with inverted Jordan triple products on groups
• Gyrogroups and homogeneous loops
• A note on sequential product of quantum effects
• Isometries of the unitary groups and Thompson isometries of the spaces of invertible positive elements in \(C^\ast\)-algebras
• Matrix multiplication is determined by orthogonality and trace
• A generalized Schwarz inequality and algebraic invariants for operator algebras
• Sequential quantum measurements
• Distances of qubit density matrices on Bloch sphere
• Characterizing sequential isomorphisms on Hilbert-space effect algebras
• A uniqueness problem of the sequence product on operator effect algebra {\cal E}(H)
• Sequential product on standard effect algebra {\cal E} (H)
• Characterization of the sequential product on quantum effects
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