Semi-discreteness and dilation theory for nest algebras Academic Article uri icon

abstract

  • In this paper it is shown that a contractive -weakly continuous Hilbert space representation of a nest algebra admits a -weakly continuous dilation to the containing algebra of all operators. This is accomplished by first establishing the complete contractivity of contractive representations through a semi-discreteness property for nest algebras relative to finite-dimensional nest algebras (Theorem 2.1). The semi-discreteness property is obtained by an examination of the order type, spectral type, and multiplicity of the nest, and by the construction of subalgebras that are completely isometric copies of finite-dimensional nest algebras, with good approximation properties. With complete contractivity at hand, the desired dilation follows from Arveson's dilation theorem and auxiliary arguments. 1988.

published proceedings

  • Journal of Functional Analysis

author list (cited authors)

  • Paulsen, V. I., Power, S. C., & Ward, J. D.

citation count

  • 10

complete list of authors

  • Paulsen, VI||Power, SC||Ward, JD

publication date

  • September 1988