On Absolute Lambert Sums

How to Compare the Absolute Values of Operator Sums and the Sums of Absolute Values?

We address the problem of comparing |A+B| and |A|+ |B| , for A,B ∈Mn(C) . Some results are obtained by using a technique of positive linear maps and several open questions are proposed. Mathematics subject classification (2010): Primary 15A60, 47A30, 47A60.

Some Binomial Sums Involving Absolute Values

We consider several families of binomial sum identities whose definition involves the absolute value function. In particular, we consider centered double sums of the form

on direct sums of baer modules

the notion of baer modules was defined recently

Choosing Smoothing Parameters For Exponential Smoothing: Minimizing Sums Of Squared Versus Sums Of Absolute Errors

Evaluation of binomial double sums involving absolute values

mostly for small positive integers k, s, t, β. In several cases, they found explicit evaluations of such sums — sometimes with proof, sometimes conjecturally. The purpose of the current paper is to provide a complete treatment of double sums of the form (1.2). More precisely, using the computer algebra package Sigma [13], we were led to the conjecture that these double sums can always be expres...