14 citations · 56 across the 37 of their papers we have counts for
17 papers · 1 filter
Lipschitz p-Approximate Schauder Frames
K. Mahesh Krishna, P. Sam Johnson
With the aim of representing subsets of Banach spaces as an infinite series using Lipschitz functions, we study a variant of metric frames which we call Lipschitz p-approximate Sch…
Non-Archimedean Welch Bounds and Non-Archimedean Zauner Conjecture
K. Mahesh Krishna
Let be a non-Archimedean (complete) valued field satisfying \begin{align*} \left|\sum_{j=1}^{n}λ_j^2\right|=\max_{1\leq j \leq n}|λ_j|^2, \quad \forall λ_j \in \mathbb…
p-adic Magic Contractions, p-adic von Neumann Inequality and p-adic Sz.-Nagy Dilation
K. Mahesh Krishna
We introduce the notion of p-adic magic contraction on p-adic Hilbert space. We derive p-adic Halmos dilation, p-adic Egervary N-dilation, p-adic von Neumann inequality and p-adic…
Continuous Non-Archimedean and p-adic Welch Bounds
K. Mahesh Krishna
We prove the continuous non-Archimedean (resp. p-adic) Banach space and Hilbert space versions of non-Archimedean (resp. p-adic) Welch bounds proved by M. Krishna. We formulate con…
Non-Archimedean and p-adic Functional Welch Bounds
K. Mahesh Krishna
We prove the non-Archimedean (resp. p-adic) Banach space version of non-Archimedean (resp. p-adic) Welch bounds recently obtained by M. Krishna. More precisely, we prove following…
Modular Bourgain-Tzafriri Restricted Invertibility Conjectures and Johnson-Lindenstrauss Flattening Conjecture
K. Mahesh Krishna
We recently formulated important Modular Bourgain-Tzafriri Restricted Invertibility Conjectures and Modular Johnson-Lindenstrauss Flattening Conjecture in the Appendix of \textit{[…
Modular Paulsen Problem and Modular Projection Problem
K. Mahesh Krishna
Based on the solution of \textbf{Paulsen Problem} by Kwok, Lau, Lee, and Ramachandran [\textit{STOC'18-Proceedings of the 50th Annual ACM SIGACT Symposium on Theory of Computing, 2…
C*-algebraic Casas-Alvero Conjecture
K. Mahesh Krishna
Based on Casas-Alvero conjecture \textit{[J. Algebra, 2001]} we formulate the following conjecture.\\ \textbf{C*-algebraic Casas-Alvero Conjecture : Let be a commutat…
C*-algebraic Smale Mean Value Conjecture and Dubinin-Sugawa Dual Mean Value Conjecture
K. Mahesh Krishna
Based on Smale mean value conjecture \textit{[Bull. Amer. Math. Soc., 1981]} and Dubinin-Sugawa dual mean value conjecture \textit{[Proc. Japan Acad. Ser. A Math. Sci., 2009]} we f…
C*-algebraic Schoenberg Conjecture
K. Mahesh Krishna
Based on Schoenberg conjecture \textit{[Amer. Math. Monthly., 1986]}/Malamud-Pereira theorem \textit{[J. Math. Anal. Appl, 2003]}, \textit{[Trans. Amer. Math. Soc., 2005]} we formu…
Metric, Schauder and Operator-Valued Frames
K. Mahesh Krishna
Notion of frames and Bessel sequences for metric spaces have been introduced. This notion is related with the notion of Lipschitz free Banach spaces. \ It is proved that every sepa…
The -problem for Approximate Schauder Frames for Banach Spaces
K. Mahesh Krishna
Motivated from the complete solution of important -problem for Gabor system for the Hilbert space by Dai and Sun [\textit{Memoirs of Amer. Math. So…
Operator-Valued p-Approximate Schauder Frames
K. Mahesh Krishna, P. Sam Johnson
We give an operator-algebraic treatment of theory of p-approximate Schuader frames which includes the theory of operator-valued frames by Kaftal, Larson, and Zhang [\textit{Trans.…
Paulsen and Projection Problems for Banach Spaces
K. Mahesh Krishna
Based on the two decades old celebrated Paulsen problem and its solutions for Hilbert spaces by Kwok, Lau, Lee, Ramachandran, Hamilton, and Moitra, we formulate Paulsen problem for…
Discrete and Continuous Welch Bounds for Banach Spaces with Applications
K. Mahesh Krishna
Let be a collection in a finite dimensional Banach space of dimension and be a collection in (dual of $\mathca…
Modular Welch Bounds with Applications
K. Mahesh Krishna
We prove the following two results. \begin{enumerate} \item Let be a unital commutative C*-algebra and be the standard Hilbert C*-module over $\mathca…
Feichtinger Conjectures, -Conjectures and Weaver's Conjectures for Banach spaces
K. Mahesh Krishna
Motivated from two decades old famous Feichtinger conjectures for frames, -conjecture and Weaver's conjecture for Hilbert spaces (and their solution by Marcus, Spiel…