TWO-NORM CONTINUOUS FUNCTIONALS ON <I>L</I></><SUB>&INFIN;</SUB>

Additive functionals on spaces with non-absolutely-continuous norm

A Geometric Estimate on the Norm of Product of Functionals

The open problem of determining the exact value of the n-th linear polarization constant cn of R n has received considerable attention over the past few years. This paper makes a contribution to the subject by providing a new lower bound on the value of sup‖y‖=1 | 〈x1,y〉 · · · 〈xn,y〉 |, where x1, . . . ,xn are unit vectors in R. The new estimate is given in terms of the eigenvalues of the Gram ...

Multiplicative Functionals on Semigroups of Continuous Functions

Let X be a compact Hausdorff space. We denote by C(X) the multiplicative semigroup of all continuous real-valued functions on X. Milgram [2] has shown that C(X) as a semigroup determines X. In this paper we investigate the set %(X) of all continuous positive nontrivial2 multiplicative functionals on C(X), where C(X) has the topology of uniform convergence. If multiplication is defined pointwise...

Constructing Ultraweakly Continuous Functionals on B(h)

In this paper we give a constructive characterisation of ultraweakly continuous linear functionals on the space of bounded linear operators on a separable Hilbert space. Let H be a separable complex Hilbert space, with orthonormal basis (en)∞n=1, and B(H) the set of bounded linear operators on H . The weak operator norm associated with the orthonormal basis (en) is defined on B(H) by ‖T ‖w ≡ ∞ ...

Recursion on the partial continuous functionals

We describe a constructive theory of computable functionals, based on the partial continuous functionals as their intendend domain. Such a task had long ago been started by Dana Scott [28], under the well-known abbreviation LCF. However, the prime example of such a theory, Per Martin-Löf’s type theory [24] in its present form deals with total (structural recursive) functionals only. An early at...