Some bounds for determinants of relatively D-stable matrices

Lower Bounds for Some Factorable Matrices

The following conjecture was posed by Axler and Shields. Let {xn} be a monotone decreasing sequence of nonnegative numbers, C the Cesáro matrix of order one. What is the best constant K for which ‖Cx‖2 ≥ K‖x‖2 for all such sequences {xn}? Lyons [3] determined that the best constant is π/ √ 6. This result was extended to p spaces for p > 1 by Bennett [1]. In [1], Bennett established the followin...

Bounds on determinants of perturbed diagonal matrices

We give upper and lower bounds on the determinant of a perturbation of the identity matrix or, more generally, a perturbation of a nonsingular diagonal matrix. The matrices considered are, in general, diagonally dominant. The lower bounds are best possible, and in several cases they are stronger than well-known bounds due to Ostrowski and other authors. If A = I−E is a real n×n matrix and the e...

Some Bounds for the Singular Values of Matrices

Abstract We know that to estimate matrix singular values ( especially the largest and the smallest ones ) is an attractive topic in matrix theory and numerical analysis. In this note, we first provide a simple estimate for the smallest singular value σn(A) of n × n positive definite matrix A. Secondly, we obtain some simple estimates for the smallest singular value σn(A) and the largest singula...

SOME BOUNDS FOR RAMIFICATION OF p-TORSION SEMI-STABLE REPRESENTATIONS

Let p be an odd prime, K a finite extension of Qp, GK = Gal(K̄/K) its absolute Galois group and e = e(K/Qp) its absolute ramification index. Suppose that T is a p-torsion representation of GK that is isomorphic to a quotient of GK -stable Zp-lattices in a semi-stable representation with HodgeTate weights {0, . . . , r}. We prove that there exists a constant μ depending only on n, e and r such th...

Lower bounds of Copson type for the transpose of matrices on weighted sequence spaces