Weak positive matrices and hyponormal weighted shifts

Quartically Hyponormal Weighted Shifts Need Not Be 3-hyponormal

We give the first example of a quartically hyponormal unilateral weighted shift which is not 3-hyponormal.

Propagation Phenomena for Hyponormal 2-variable Weighted Shifts

We study the class of hyponormal 2-variable weighted shifts with two consecutive equal weights in the weight sequence of one of the coordinate operators. We show that under natural assumptions on the coordinate operators, the presence of consecutive equal weights leads to horizontal or vertical flatness, in a way that resembles the situation for 1-variable weighted shifts. In 1variable, it is w...

Hyponormal matrices and semidefinite invariant subspaces in indefinite inner products

It is shown that, for any given polynomially normal matrix with respect to an indefinite inner product, a nonnegative (with respect to the indefinite inner product) invariant subspace always admits an extension to an invariant maximal nonnegative subspace. Such an extension property is known to hold true for general normal matrices if the nonnegative invariant subspace is actually neutral. An e...

Quasihyponormal and strongly hyponormal matrices in inner product spaces

Interval Weighted Comparison Matrices – A Review

Nowadays, interval comparison matrices (ICM) take an important role in decision making under uncertainty. So it seems that a brief review on solution methods used in ICM should be useful. In this paper, the common methods are divided into four categories that are Goal Programming Method (GPM), Linear Programming Method (LPM), Non-Linear Programming Method (NLPM) and Statistic Analysis (SA). GPM...