Every $C$-symmetric Banach $*$-algebra is symmetric

On Asymptotically Symmetric Banach Spaces

A Banach space X is asymptotically symmetric (a.s.) if for some C <∞, for all m ∈ N, for all bounded sequences (xj)j=1 ⊆ X, 1 ≤ i ≤ m, for all permutations σ of {1, . . . ,m} and all ultrafilters U1, . . . ,Um on N, lim n1,U1 . . . lim nm,Um ∥∥∥∥ m ∑ i=1 xini ∥∥∥∥ ≤ C lim nσ(1),Uσ(1) . . . lim nσ(m),Uσ(m) ∥∥∥∥ m ∑

Review: A C*-algebra approach to complex symmetric operators

The C*-algebra of Symmetric Words in Two Universal Unitaries

We compute the K-theory of the C*-algebra of symmetric words in two universal unitaries. This algebra is the fixed point C*-algebra for the order-two automorphism of the full C*algebra of the free group on two generators which switches the generators. Our calculations relate the K -theory of this C*-algebra to the K-theory of the associated C*-crossed-product by Z2.

Every Banach Space is Reflexive

The title above is wrong, because the strong dual of a Banach space is too strong to assert that the natural correspondence between a space and its bidual is an isomorphism. This, from a categorical point of view, is indeed the right duality concept because it yields a self adjoint dualisation functor. However, for many applications the non–reflexiveness problem can be solved by replacing the n...

00 5 on Asymptotically Symmetric Banach Spaces

A Banach space X is asymptotically symmetric (a.s.) if for some C < ∞, for all m ∈ N, for all bounded sequences (x i j)