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arXiv · 2108.06662

C*-algebraic Schur product theorem, P\'{o}lya-Szeg\H{o}-Rudin question and Novak's conjecture

K. Mahesh Krishna
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Abstract

Striking result of Vyb\'{\i}ral [\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. Vyb\'{\i}ral used this result to prove the Novak's conjecture. In this paper, we define Schur product of matrices over arbitrary C*-algebras and derive the results of Schur and Vyb\'{\i}ral. As an application, we state C*-algebraic version of Novak's conjecture and solve it for commutative unital C*-algebras. We formulate P\'{o}lya-Szeg\H{o}-Rudin question for the C*-algebraic Schur product of positive matrices.

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K. Mahesh Krishna. 2021-08-15. C*-algebraic Schur product theorem, P\'{o}lya-Szeg\H{o}-Rudin question and Novak's conjecture. https://doi.org/10.4134/jkms.j210627

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