Concept

Cotlar–Stein lemma

Summary
In mathematics, in the field of functional analysis, the Cotlar–Stein almost orthogonality lemma is named after mathematicians Mischa Cotlar and Elias Stein. It may be used to obtain information on the operator norm on an operator, acting from one Hilbert space into another when the operator can be decomposed into almost orthogonal pieces. The original version of this lemma (for self-adjoint and mutually commuting operators) was proved by Mischa Cotlar in 1955 and allowed him to conclude that the Hilbert transform is a continuous linear operator in L^2 without using the Fourier transform. A more general version was proved by Elias Stein. Cotlar–Stein almost orthogonality lemma Let E,,F be two Hilbert spaces. Consider a family of operators T_j, j\geq 1, with each T_j a bounded linear operator from E to F. Denote : a_{jk}=\Vert T_j T_k^\ast\Vert, \qquad b_{jk}=\Vert T_j^\ast T_
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