Acting Semicircular Elements Induced by Orthogonal Projections on Von-Neumann-Algebras

Linear maps on von-Neumann algebras behaving like anti-derivations at orthogonal elements

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Nonlinear $*$-Lie higher derivations on factor von Neumann algebras

Let $mathcal M$ be a factor von Neumann algebra. It is shown that every nonlinear $*$-Lie higher derivation$D={phi_{n}}_{ninmathbb{N}}$ on $mathcal M$ is additive. In particular, if $mathcal M$ is infinite type $I$factor, a concrete characterization of $D$ is given.

Linear Combinations of Projections in Von Neumann Algebras

Any operator in a von Neumann algebra is a linear combination of a finite number of projections from the algebra with coefficients from the center of the algebra. Those von Neumann algebras that are the complex linear span of their projections are identified.

Notes on von Neumann algebras

On the Diagonals of Projections in Matrix Algebras Over Von Neumann Algebras

ON THE DIAGONALS OF PROJECTIONS IN MATRIX ALGEBRAS OVER VON NEUMANN ALGEBRAS Soumyashant Nayak Richard V. Kadison The main focus of this dissertation is on exploring methods to characterize the diagonals of projections in matrix algebras over von Neumann algebras. This may be viewed as a non-commutative version of the generalized Pythagorean theorem and its converse (Carpenter’s Theorem) studie...