20 papers
Octonionic Kittaneh Numerical Radius Inequalities
K. Mahesh Krishna
We show that for certain classes of matrices over octonions, a weak version of breakthrough numerical radius inequalities obtained by Kittaneh [\textit{{Stud. Math.}, 2005}] hold.
Morphisms of double Lie groupoids: a simplicial approach
Daniel Álvarez, Kalin Krishna, Stefano Ronchi
Motivated by recent developments in generalized Kähler geometry, we study morphisms of double Lie groupoids from a simplicial viewpoint. We show that the codiagonal functor $\Wbar$…
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 Cauchy-Schwarz Angle-Length and Chebyshev Arithmetic Mean Inequalities
K. Mahesh Krishna
Let be a non-Archimedean valued field. Let . For every , we show that \begin{align*} \left|\sum_{j=1}^…
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…
Finite Field Tarski-Maligranda Inequalities
K. Mahesh Krishna
Let be a sub-modulus field such that . Let be a sub-normed linear space over . Then we show that \begin{align*} \bigg|\|x\|-\|y\|\b…
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…
Non-Archimedean Brauer Oval (of Cassini) Theorem and Applications
K. Mahesh Krishna
Nica and Sprague [\textit{Am. Math. Mon., 2023}] derived a non-Archimedean version of the Gershgorin disk theorem. We derive a non-Archimedean version of the oval (of Cassini) theo…
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…
Continuous Donoho-Elad Spark Uncertainty Principle
K. Mahesh Krishna
Donoho and Elad \textit{[Proc. Natl. Acad. Sci. USA, 2003]} introduced the important notion of the spark of a frame, using which they derived a fundamental uncertainty principle. B…
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…
Modular Deutsch Entropic Uncertainty Principle
K. Mahesh Krishna
Khosravi, Drnovšek and Moslehian [\textit{Filomat, 2012}] derived Buzano inequality for Hilbert C*-modules. Using this inequality we derive Deutsch entropic uncertainty principle f…
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…
Indefinite Halmos, Egervary and Sz.-Nagy Dilations
K. Mahesh Krishna
Let be an indefinite inner product module over a *-ring of characteristic 2. We show that every self-adjoint operator on admits Halmos, Egervary and Sz.…
C*-algebraic Gauss-Lucas Theorem and C*-algebraic Sendov's Conjecture
K. Mahesh Krishna
Using a result of Robertson \textit{[Proc. Edinburgh Math. Soc. (2), 1976]}, we introduce a notion of differentiation of maps on certain classes of unital commutative C*-algebras.…
C*-algebraic Schur product theorem, Pólya-Szegő-Rudin question and Novak's conjecture
K. Mahesh Krishna
Striking result of Vyb\'ıral [\textit{Adv. Math.} 2020] says that Schur product of positive matrices is bounded below by the size of the matrix and the row sums of Schur product. V…