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Aluthge Transformation
Aluthge may refer to: *Aluthge transform In mathematics and more precisely in functional analysis, the Aluthge transformation is an operation defined on the set of bounded operators of a Hilbert space. It was introduced by Ariyadasa Aluthge to study p-hyponormal linear operators. Defi ..., mathematics concept * Asela Aluthge (born 1987), Sri Lankan cricketer {{Disambiguation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Aluthge Transform
In mathematics and more precisely in functional analysis, the Aluthge transformation is an operation defined on the set of bounded operators of a Hilbert space. It was introduced by Ariyadasa Aluthge to study p-hyponormal linear operators. Definition Let H be a Hilbert space and let B(H) be the algebra of linear operators from H to H. By the polar decomposition theorem, there exists a unique partial isometry Partial may refer to: Mathematics *Partial derivative, derivative with respect to one of several variables of a function, with the other variables held constant ** ∂, a symbol that can denote a partial derivative, sometimes pronounced "partial ... U such that T=U, T, and \ker(U)\supset\ker(T), where , T, is the square root of the operator T^*T. If T\in B(H) and T=U, T, is its polar decomposition, the Aluthge transform of T is the operator \Delta(T) defined as: : \Delta(T)=, T, ^U, T, ^. More generally, for any real number \lambda\in ,1/math>, the \lam ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |