L-subinvariant norms

L norms of trigonometric polynomials

Markoff-type Inequalities in Weighted L-norms

We give exact estimations of certain weighted L-norms of the k-th derivative of polynomials which have a curved majorant. They are all obtained as applications of special quadrature formulae.

Counting Cycles and Finite Dimensional L Norms

We obtain sharp bounds for the number of n–cycles in a finite graph as a function of the number of edges, and prove that the complete graph is optimal in more ways than could be imagined. We prove sharp estimates on both ∑n i=1 x k i and ∑n i=1 |xi|, subject to the constraints that ∑n i=1 x 2 i = C and ∑n i=1 xi = 0. Introduction This note was inspired by the following question, which had been ...

Norms of Positive Operators on L-spaces

Let 0 ≤ T : L(Y, ν) → L(X,μ) be a positive linear operator and let ‖T‖p,q denote its operator norm. In this paper a method is given to compute ‖T‖p,q exactly or to bound ‖T‖p,q from above. As an application the exact norm ‖V ‖p,q of the Volterra operator V f(x) = ∫ x 0 f(t)dt is computed. Department of Mathematics, University of South Carolina, Columbia, SC 29208 1991 Mathematics Subject Classi...

Correspondence between probabilistic norms and fuzzy norms

In this paper, the connection between Menger probabilistic norms and H"{o}hle probabilistic norms is discussed. In addition, the correspondence between probabilistic norms and Wu-Fang fuzzy (semi-) norms is established. It is shown that a probabilistic norm (with triangular norm $min$) can generate a Wu-Fang fuzzy semi-norm and conversely, a Wu-Fang fuzzy norm can generate a probabilistic norm.