Local automorphisms of standard operator algebras

Let X be an infinite-dimensional separable real or complex Banach space and A a closed standard operator algebra on X. Then every local automorphism of A is an automorphism. The assumptions of infinite-dimensionality, separability, and closeness are all indispensable.     

On K_0-groups of operator algebras on Banach spaces

This paper merges some classifications of G-M-type Banach spaces simplifically, discusses the condition of K0(B(X)) = 0 for operator algebra B(X) on a Banach space X, and obtains a result to improve Laustsen's sufficient condition, gives an example to show that X ≈ X2 is not a sufficient condition of K0(B(X)) = 0.     

Some G-M-type Banach spaces and K-groups of operator algebras on them

By providing several new varieties of G-M-type Banach spaces according todecomposable and compoundable properties, this paper discusses the operator structuresof these spaces and the K-theory of the algebra of the operators on these G-M-type Ba-nach spaces through calculation of the K-groups of the operator ideals contained in theclass of Riesz operators.     

On local automorphisms of group algebras of compact groups

We show that with few exceptions every local isometric automorphism of the group algebra of a compact metric group is an isometric automorphism.

     

Some characterizations of the automorphisms of

We present some nonlinear characterizations of the automorphisms of the operator algebra and the function algebra by means of their spectrum preserving properties.

     

A note on local automorphisms

Let H be an infinite-dimensional almost separable Hilbert space. We show that every local automorphism of ℬ(H), the algebra of all bounded linear operators on a Hilbert space H, is an automorphism.     

On K0-groups of operator algebras on Banach spaces

This paper merges some classifications of G-M-type Banach spaces simplifically, discusses the condition of K ₀(B(X)) = 0 for operator algebra B(X) on a Banach space X, and obtains a result to improve Laustsen's sufficient condition, gives an example to show that X ≈ X ² is not a sufficient condition of K ₀(B(X)) = 0.     

Lax operator algebras

In this paper, we develop the general approach, introduced in [l], to Lax operators on algebraic curves. We observe that the space of Lax operators is closed with respect to their usual multiplication as matrix-valued functions. We construct orthogonal and symplectic analogs of Lax operators, prove that they form almost graded Lie algebras, and construct local central extensions of these Lie algebras.     

Bilocal derivations of standard operator algebras

In this paper, we shall show the following two results: (1) Let be a standard operator algebra with , if is a linear mapping on which satisfies that maps into for all , then is of the form for some in . (2) Let be a Hilbert space, if is a norm-continuous linear mapping on which satisfies that maps into for all self-adjoint projection in , then is of the form for some in .

     

Commutants of certain analytic operator algebras

We prove that algebraic commutants of maximal subdiagonal algebras and of analytic operator algebras determined by flows in a -finite von Neumann algebra are self-adjoint.

     

Fredholm composition operators on algebras of analytic functions on Banach spaces

We prove that Fredholm composition operators acting on the uniform algebra H^∞(BE) of bounded analytic functions on the open unit ball of a complex Banach space E with the approximation property are invertible and arise from analytic automorphisms of the ball.     

算子代数上导子空间的拓扑自反性

It is proved that the spaces of derivations on some operator algebras are topologically reflexive in the weak operator topology.     

Local conformal nets arising from framed vertex operator algebras

We apply an idea of framed vertex operator algebras to a construction of local conformal nets of (injective type III₁) factors on the circle corresponding to various lattice vertex operator algebras and their twisted orbifolds. In particular, we give a local conformal net corresponding to the moonshine vertex operator algebras of Frenkel-Lepowsky-Meurman. Its central charge is 24, it has a trivial representation theory in the sense that the vacuum sector is the only irreducible DHR sector, its vacuum character is the modular invariant J-function and its automorphism group (the gauge group) is the Monster group. We use our previous tools such as α-induction and complete rationality to study extensions of local conformal nets.     

On K 0-groups of operator algebras on Banach spaces

This paper merges some classifications of G-M-type Banach spaces simplifically, discusses the condition of K ₀(B(X)) = 0 for operator algebra B(X) on a Banach space X, and obtains a result to improve Laustsen's sufficient condition, gives an example to show that X ≈ X ² is not a sufficient condition of K ₀(B(X)) = 0.     

Isomorphism problems and groups of automorphisms for generalized Weyl algebras

We present solutions to isomorphism problems for various generalized Weyl algebras, including deformations of type-A Kleinian singularities and the algebras similar to introduced by S. P. Smith. For the former, we generalize results of Dixmier on the first Weyl algebra and the minimal primitive factors of by finding sets of generators for the group of automorphisms.

     

On the simplicial cohomology of Banach operator algebras

We investigate the simplicial cohomology of certain Banach operator algebras. The two main examples considered are the Banach algebra of all bounded operators on a Banach space and its ideal of approximable operators. Sufficient conditions will be given forcing Banach algebras of this kind to be simplicially trivial.     

Local automorphisms of semisimple algebras and group algebras

Let F be a field of characteristic not 2, and let A be a finite-dimensional semisimple F -algebra. All local automorphisms of A are characterized when all the degrees of A are larger than 1. If F is further assumed to be an algebraically closed field of characteristic zero, K a finite group, F K the group algebra of K over F , then all local automorphisms of F K are also characterized.