Abstract
We prove that a matrix is continuous if and only if it is spanned by its diagonals, even when the concept of continuity for matrices is extended to infinite block matrices belonging to normed ideal generated by a given unitarily invariant norm. We also prove a block matrix generalization of Bernstein inequality: and for any unitarily invariant norm |||·||| and for every [X mn ] m,n∈ℤ ∈ 𝒞|||·|||(ℋ) such that for some N ∈ ℕ it satisfy X mn = 0 for all |m − n| > N.
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