ИСТИНА

Estimates of operator norms of submatrices of a given matrix A find applications in various areas of mathematics, for instance, in computational methods and discretization. One of the first results on this topic was obtained in [1]. There the estimates for the classical operator norm of submatrices are a concequence of the corresponding estimates for (2, 1)-norms. The case of (2, 1)-norm was studied in [2] in details. It contains the partial answer to the Srivastava's question arosen in his research blog (https://math.berkeley.edu/ nikhil/courses/270/open.pdf). Now we consider conditions on a matrix A with unit operator (𝑝, 𝑞)-norm ensuring the existence of a partition of this matrix into two submatrices with (𝑝, 𝑞)-norms close to 1/2^(1/𝑞). [1] B. S. Kashin, Some properties of matrices of bounded operators from the space 𝑙_2^n into 𝑙_2^m. Izv. Akad. Nauk. Armyan. SSR Ser. Mat. 15(5), 379-394 (1980) [2] B. S. Kashin, I. V. Limonova, Decomposing a Matrix into two Submatrices with Extremally Small (2,1)-norm. Math. Notes, 106:1 (2019), 63-70.