Let ǫ > 0 be a positive number. Is there a number δ > 0 satisfying the following? Given any pair of unitaries u and v in a unital simple C∗-algebra A with [v] = 0 in K1(A) for which ‖uv − vu‖ < δ, there is a continuous path of unitaries {v(t) : t ∈ [0, 1]} ⊂ A such that v(0) = v, v(1) = 1 and ‖uv(t)− v(t)u‖ < ǫ for all t ∈ [0, 1]. An answer is given to this question when A is assumed to be a un...

We show that if T is an isometry (as metric spaces) from an open subgroup of the invertible group A of a unital Banach algebra A onto an open subgroup of the invertible group B of a unital Banach algebra B, then T is extended to a real-linear isometry up to translation between these Banach algebras. We consider multiplicativity or unti-multiplicativity of the isometry. Note that a unital linear...

let a be a unital algebra over a field of characteristic zero. we show that every derivation from( ) n m a into its dual ( ) n m a ∗ is the sum of an inner derivation and a derivation induced by a derivationfrom a into a∗

we define a new type of spectrum, called δ-approximate spectrum, of an element a in a complex unital banach algebra a and show that the δ-approximate spectrum σ_δ (a) of a is compact. the relation between the δ-approximate spectrum and the usual spectrum is investigated. also an analogue of the classical gleason-kahane-zelazko theorem is established: for each ε>0, there is δ>0 such that if ϕ is...

This paper presents a construction of very high-rate low-density parity-check (LDPC) codes based on the incidence matrices of unital designs. Like the projective geometry and oval designs, unital designs exist with incidence matrices which are significantly rank deficient. Thus high-rate LDPC codes with a large number of linearly dependent parity-check equations can be constructed. The LDPC cod...

(Day 1): References (for general background) →Varieties of lattice-ordered groups, N. R. Reilly, in Lattice-Ordered Groups, Advances and Techniques, A. M. W. Glass and W. C. Holland (eds.), Kluwer Academic Publishers, 1989. Lattice-Ordered Groups, an Introduction, M. Anderson and T. Feil, D. Reidel Pub. Co., 1988. Theory of Lattice-Ordered Groups, M. Darnel, Marcel Dekker, 1995. Partially Order...