Mazur’s theorem on sequentially continuous linear functionals

The sequentially realizable functionals

We consider a notion of sequential functional of -nite type, more generous than the familiar notion embodied in Plotkin’s language PCF. We study both the “full” and “e4ective” partial type structures arising from this notion of sequentiality. The full type structure coincides with that given by the strongly stable model of Bucciarelli and Ehrhard; it has also been characterized by van Oosten in...

Sequentially Continuous Linear Mappings in Constructive Analysis

Cdmtcs Research Report Series Sequentially Continuous Linear Mappings in Constructive Analysis Sequentially Continuous Linear Mappings in Constructive Analysis

Computable Jordan Decomposition of Linear Continuous Functionals on $C[0;1]$

By the Riesz representation theorem using the Riemann-Stieltjes integral, linear continuous functionals on the set of continuous functions from the unit interval into the reals can either be characterized by functions of bounded variation from the unit interval into the reals, or by signed measures on the Borel-subsets. Each of these objects has an (even minimal) Jordan decomposition into non-n...

Characterising Weak - Operator Continuous Linear Functionals on B ( H ) constructively

Abstract. Let B(H) be the space of bounded operators on a notnecessarily-separable Hilbert space H . Working within Bishop-style constructive analysis, we prove that certain weak-operator continuous linear functionals on B(H) are finite sums of functionals of the form T 〈Tx, y〉. We also prove that the identification of weakand strong-operator continuous linear functionals on B(H) cannot be esta...