© 2019, Pleiades Publishing, Ltd. The problem of automatic additivity of Jordan type homomorphisms has received a great deal of attention in theory of operator algebras as well in ring theory. We study additivity of quadratic ...

The interplay between order-theoretic properties of structures of subspaces affiliated with a von Neumann algebra M and the inner structure of the algebra M is studied. The following characterization of finiteness is given: ...

© 2014, Pleiades Publishing, Ltd. We show that any spectral lattice orthoautomorphism of the structure of positive contractions on a von Neumann algebra, endowed with the spectral order and orthogonality relation, that ...

© 2019, Springer Science+Business Media, LLC, part of Springer Nature. We show that ordinal isomorphisms of orthogonal measures on state spaces of operator algebras equipped with the Choquet order are generated by Jordan ...

© 2016 Mathematical Institute Slovak Academy of Sciences.The paper deals with inner product spaces generated by states on Jordan algebras. We show an interplay between completeness of the Gelfand-Neumark-Segal representation ...

© 2020, Pleiades Publishing, Ltd. Abstract: The paper deals with quasi linear maps on two by two matrices over Banach and $$C^{\ast}$$-algebras. Let $$\varphi:A\to X$$ be a homogeneous map between Banach algebra $$A$$ and ...

© 2016, Springer Science+Business Media New York.An interplay between recent topos theoretic approach and standard convex theoretic approach to quantum theory is discovered. Combining new results on isomorphisms of posets ...

© 2017 Springer Science+Business Media New YorkQuantum symmetries of spectral lattices are studied. Basic properties of spectral order on AW∗-algebras are summarized. Connection between projection and spectral automorphisms ...

Abstract: We study the poset of partial isometries in C*-algebras endowed with the *-order and *-orthogonality. We show that this structure is a complete Jordan invariant for AW*-algebras. We prove that partial isometries ...