INTERPOLATION OF STATES BY VECTOR STATES ON CERTAIN OPERATOR-ALGEBRAS Academic Article uri icon

abstract

  • Let T be an operator on an infinite dimensional Hilbert space {Mathematical expression} with eigenvectors vi, {norm of matrix}vi{norm of matrix}=1, i=1, 2, ..., and sp{vi{curly logical or}in} dense in {Mathematical expression}. Suppose that {vi} is a Schauder basis for {Mathematical expression}. We denote by ATthe ultraweakly closed algebra generated by T and I, the identity operator on {Mathematical expression}. For any nonnegative sequence of scalars {Mathematical expression}, we associate an ultraweakly (normal) continuous linear functional {Mathematical expression} where {Mathematical expression}, and {Mathematical expression} for all AAT. We denote the set of all such linear functionals on ATby F(T). The question that we investigate in this paper is whether each linear functional in F(T) is a vector state, i.e. does =x for some unit vector x in {Mathematical expression}? 1988 Birkhuser Verlag.

published proceedings

  • INTEGRAL EQUATIONS AND OPERATOR THEORY

author list (cited authors)

  • TSUI, S. K., & WARD, J. D.

citation count

  • 0

complete list of authors

  • TSUI, SK||WARD, JD

publication date

  • March 1988