The eigenvalues of a self-adjoint nÃ—n matrix A can be put into a decreasing sequence Î» = (Î»1, . . . , Î»n), with repetitions according to multiplicity, and the diagonal of A is a point of R that bearsâ€¦ (More)

Proceedings of the National Academy of Sciencesâ€¦

2002

The Pythagorean Theorem and variants of it are studied. The variations evolve to a formulation in terms of noncommutative, conditional expectations on von Neumann algebras that displays the theoremâ€¦ (More)

Proceedings of the National Academy of Sciencesâ€¦

2002

The study of the Pythagorean Theorem and variants of it as the basic result of noncommutative, metric, Euclidean Geometry is continued. The emphasis in the present article is the case of infiniteâ€¦ (More)

This paper concerns Banach algebras which are real or * algebras and possess a unit. The principal method of attack is via an ordering of the algebra, the positive cone being the closure of the setâ€¦ (More)

A class of algebras is introduced that includes the unital Banach algebras over the complex numbers. Commutator results are proved for such algebras and used to establish spectral properties ofâ€¦ (More)

It is known that a continuous family of compact operators can be diagonalized pointwise. One can consider this fact as a possibility of di-agonalization of the compact operators in Hilbert modulesâ€¦ (More)

The infinite-dimensional analogues of the classical general linear group appear as groups of invertible elements of Banach algebras. Mappings of these groups onto themselves that extend to affineâ€¦ (More)

The cohomology of operator algebras introduced by B. E. Johnson, R. V. Kadison, and J. R. Ringrose in a series of three papers is a useful tool for obtaining new invariants for operator algebras orâ€¦ (More)

We study some of the possibilities for formulating the Heisenberg relation of quantum mechanics in mathematical terms. In particular, we examine the framework discussed by Murray and von Neumann, theâ€¦ (More)