22 citations · 43 across the 17 of their papers we have counts for
5 papers · 1 filter
Convergence of functions of self-adjoint operators and applications
Lawrence G. Brown
The main result (roughly) is that if (H_i) converges weakly to H and if also f(H_i) converges weakly to f(H), for a single strictly convex continuous function f, then (H_i) must co…
A treatment of strongly operator convex functions that does not require any knowledge of operator algebras
Lawrence G. Brown
In [B1, Theorem 2.36] we proved the equivalence of six conditions on a continuous function f on an interval. These conditions define a subset of the set of operator convex function…
Nearly relatively compact projections in operator algebras
Lawrence G. Brown
Let A be a C*-algebra and A** its enveloping von Neumann algebra. C. Akemann suggested a kind of non-commutative topology in which certain projections in A** play the role of open…
Some directed subsets of C*-algebras and semicontinuity theory
Lawrence G. Brown
The main result concerns a sigma-unital C*-algebra A, a strongly lower semicontinuous element h of A**, the enveloping von Neumann algebra, and the set of self-adjoint elements a o…
Some Automatic Continuity Theorems for Operator Algebras and Centralizers of Pedersen's Ideal
Lawrence G. Brown
We prove automatic continuity theorems for "decomposable" or "local" linear transformations between certain natural subspaces of operator algebras. The transformations involved are…