10 papers · 1 filter
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…
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…
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 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…
A Functional Version of the Sparsity Theorem
K. Mahesh Krishna
Celebrated breakthrough sparsity theorem obtained independently by Donoho and Elad \textit{[Proc. Natl. Acad. Sci. USA, 2003]} and Gribonval and Nielsen \textit{[IEEE Trans. Inform…
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 \b…
Product Entropic Uncertainty Principle
K. Mahesh Krishna
Motivated from Deutsch entropic uncertainty principle and several product uncertainty principles, we derive an uncertainty principle for the product of entropies using functions.
Noncommutative Donoho-Elad-Gribonval-Nielsen-Fuchs Sparsity Theorem
K. Mahesh Krishna
Breakthrough Sparsity Theorem, derived independently by Donoho and Elad \textit{[Proc. Natl. Acad. Sci. USA, 2003]}, Gribonval and Nielsen \textit{[IEEE Trans. Inform. Theory, 2003…
Algebraic Andô Dilation
K. Mahesh Krishna
We solve the Andô dilation problem for linear maps on vector space asked by Krishna and Johnson in \textit{[Oper. Matrices, 2022]}. More precisely, we show that any commuting linea…