This paper gives double angle theorems that bound the change in an invariant subspace of an indefinite Hermitian matrix in the graded form H = D∗AD subject to a perturbation H → H̃ = D∗(A+ A)D. These theorems extend recent results on a definite Hermitian matrix in the graded form (Linear Algebra Appl. 311 (2000) 45) but the bounds here are more complicated in that they depend on not only relativ...

Pseudo-MTL algebras or weak pseudo-BL algebras are non-commutative fuzzy structures which arise from pseudo-t-norms, namely, pseudo-BL algebras without the pseudo-divisibility condition. The aim of this paper is to investigate the properties of pseudo-BL algebras that also hold for pseudoMTL algebras. We will also study some classes of pseudo-MTL algebras such as good, local and Archimedean pse...

In this paper we develop a theory for analysing the size of a Lie bracket or commutator in a matrix Lie algebra. Complete details are given for the Lie algebra so(n) of skew symmetric matrices. 1 Norms and commutators in Mn[R] and so(n) This paper is concerned with the following question. Let g be a Lie algebra (Carter, Segal & Macdonald 1995, Humphreys 1978, Varadarajan 1984). Given X,Y ∈ g an...

Let I = ([0; 1];_;^; 0; 1), where _ and ^ are max and min, respectively. This algebra is the basic building block of fuzzy set theory and logic. Likewise, the algebra I = ([0; 1];_;^; 0; 1), where [0; 1] = f(a; b) : a; b 2 [0; 1], a bg, _, ^ are given coordinate-wise, and 0 and 1 are the bounds on [0; 1], is the relevant algebra for interval-valued fuzzy set theory and logic. A good share of th...

We study the efficient numerical solution of infinite matrix equations Au = f for a matrix A in the Jaffard algebra. These matrices appear naturally via frame discretizations in many applications such as Gabor analysis, sampling theory, and quasi-diagonalization of pseudo-differential operators in the weighted Sjöstrand class. The proposed algorithm has two main features: firstly, it converges ...

In this paper, we deal with Molaei’s generalized groups. We definethe notion of a fuzzy generalized subgroup with respect to a t-norm (orT-fuzzy generalized subgroup) and give some related properties. Especially,we state and prove the Representation Theorem for these fuzzy generalizedsubgroups. Next, using the concept of continuity of t-norms we obtain a correspondencebetween TF(G), the set of ...

For any complex valued functions over topological space F there exists a relation in von Neumann algebras of *-graded that is bounded on compact Hausdorff where for category- I, II, III commutative form 〖AW〗^* such to satisfy monotone complete C^* algebra suffice an isomorphic factor f the same tamed as W^* having generators η generic group η(G) 2-groups G_+ and G_- former being additive intege...