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This page lists the top ten most read articles for this journal based on the number of full text views and downloads recorded on Cambridge Core over the last 30 days. This list is updated on a daily basis.
Trace inequalities for sums and products of matrices are presented. Relations between the given inequalities and earlier results are discussed. Among other inequalities, it is shown that if A and B are positive semidefinite matrices then for any positive integer k.
Let A and B be n × n matrices over the real or complex field. Lower and upper bounds for |det(A + B)| are given in terms of the singular values of A and B. Extension of our techniques to estimate |f(A + B)| for other scalar-valued functions f on matrices is also considered.
In [1], Theorem 6, a sufficient condition is given for a multifunction to be “of Souslin type”. However, the proof contains an error; we are required to prove that the multifunction Ω: S→ P×NN defined by
has values which are closed subsets of P×NN (the notation is explained in [1]). The “proof” of this fact given in [1] is manifestly incorrect as it appears to assume that NN has the discrete topology.
The familiar notion of the determinant is generalised to include rectangular matrices. An expression for a normalised generalised inverse of a matrix is given in terms of its determinant and a possible generalisation of the Schur complement is discussed as a simple application.
Let A be the class of functions f(z) which are analytic in the unit disk U with f(0) = f′(0) - 1 = 0. A subclass S(λ, M) (λ > 0, M > 0) of A is introduced. The object of the present paper is to prove some interesting convolution properties of functions f(z) belonging to the class S(λ, M). Also a certain integral operator J for f(z) in the class A is considered.
We generalise some existing results on strict radical classes, and introduce some new notions of hereditariness of radical classes. This is achieved by considering the classes of rings for which a radical class is hereditary and/or strict (in the general sense).
Some inequalities in terms of the Gâteaux derivatives related to Jensen’s inequality for convex functions defined on linear spaces are given. Applications for norms, mean f-deviations and f-divergence measures are provided as well.
A topological space is said to be locally dyadic if every neighbourhood of a point contains a dyadic neighbourhood of that point. It is proved here that every locally compact Hausdorff topological group is locally dyadic.
It is shown that a condition of Kurzwell concerning fixed-points of certain operators on a finite group G is sufficient to ensure that G is soluble. The result generalizes those of Martineau on elementary abelian fixed-point-free operator groups.