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Quaternionic Kittaneh Numerical Radius Inequalities
K. Mahesh Krishna
We show that for certain classes of matrices over quaternions, a more restrictive version of breakthrough numerical radius inequalities obtained by Kittaneh [\textit{{Stud. Math.},…
Non-Archimedean Massera-Schaffer-Maligranda-Pecaric-Rajic Inequality
K. Mahesh Krishna
Massera and Schaffer [\textit{Ann. Math. (2), 1958}] derived a breakthrough upper bound for the Clarkson angle between two nonzero vectors in a normed linear space, which was later…
Non-Archimedean Tarski-Maligranda Inequalities
K. Mahesh Krishna
In 1930, Tarski observed that \begin{align*} \bigg||r|-|s|\bigg|=|r-s|+ |r+s|-(|r|+|s|), \quad \forall r, s \in \mathbb{R}. \end{align*} In 2008, Maligranda converted the previous…
Noncommutative Cauchy Bound and Noncommutative Montel Bound for Roots of Polynomials
K. Mahesh Krishna
In 1829, Cauchy derived an upper bound for every root of a complex polynomial using the maximum of the absolute values of the coefficients. In 1931, Montel derived an upper bound u…
p-adic Ghobber-Jaming Uncertainty Principle
K. Mahesh Krishna
Let and be two orthonormal bases for a finite dimensional p-adic Hilbert space . Let be such that…
Noncommutative Spherical Codes
K. Mahesh Krishna
Spherical codes, with a rich history spanning nearly five centuries, remain an area of active mathematical exploration and are far from being fully understood. These codes, which a…