Abstract. In 1990 the second author constructed a basis for the centre of the Hecke algebra of the symmetric group Sn over Q[ξ] using norms [13]. An integral “minimal” basis was later given by the first author in 1999 [5], following [9]. In principle one can then write elements of the norm basis as integral linear combinations of minimal basis elements. In this paper we find an explicit non-rec...

The study of linear algebra has become more and more popular in the last few decades. People are attracted to this subject because of its beauty and its connections with many other pure and applied areas. In theoretical development of the subject as well as in many applications, one often needs to measure the “length” of vectors. For this purpose, norm functions are considered on a vector space...

The convergence of numerical approximations to the solutions of differential equations is a key aspect of Numerical Analysis and Scientific Computing. Iterative solution methods for the systems of linear(ised) equations which often result are also underpinned by analyses of convergence. In the function space setting, it is widely appreciated that there are appropriate ways in which to assess co...

This paper is concerned with Wiener-Hopf integral operators on Lp and with Toeplitz operators (or matrices) on lp. The symbols of the operators are assumed to be continuous matrix functions. It is well known that the invertibility of the operator itself and of its associated operator imply the invertibility of all sufficiently large truncations and the uniform boundedness of the norms of their ...

This paper gives double angle theorems that bound the change in an invariant subspace of an indeenite Hermitian matrix in the graded form H = D AD subject to a perturbation H ! e H = D (A + A)D. These theorems extend recent results on a deenite Hermitian matrix in the graded form (Linear Algebra Appl., 311 (2000), 45{60) but the bounds here are more complicated in that they depend on not only r...

Contour lines totally fix the structure of leftcontinuous t-norms. For each t-norm, these contour lines are determined by the corresponding residual implicator. Most properties involving residual implicators can now easily be translated into properties involving contour lines. As the portation law expresses associativity, we dispose of a powerful tool for constructing left-continuous t-norms. I...

Perturbation bounds in numerical linear algebra are traditionally derived and expressed using norms. Norm bounds cannot reeect the scaling or sparsity of a problem and its perturbation, and so can be unduly weak. If the problem data and its perturbation are measured componentwise, much smaller and more revealing bounds can be obtained. A survey is given of componentwise perturbation theory in n...

This paper presents a solution to a problem from superanalysis about the existence of Hilbert-Banach superalgebras. Two main results are derived: 1) There exist Hilbert norms on some graded algebras (infinite-dimensional superalgebras included) with respect to which the multiplication is continuous. 2) Such norms cannot be chosen to be submultiplicative and equal to one on the unit of the algeb...