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math.FA2022
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…
math.RA2022
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.…
math.OA2022
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.…