N Congruency of Operators
We use a combination of modified Newton method and Tikhonov regularization to obtain a stable approximate solution for nonlinear ill-posed Hammerstein-type operator equations KF(x) = y. It is assumed that the available data is with , K: Z → Y is a bounded linear operator and F: X → Z is a nonlinear operator where X,Y,Z are Hilbert spaces. Two cases of F are considered: where exists (F’(x₀) is the Fréchet derivative of F at an initial guess x₀) and where F is a monotone operator. The parameter...
Let be a Banach space of analytic functions on the open unit disk and a subset of linear isometries on . Sufficient conditions are given for non-supercyclicity of . In particular, we show that the semigroup of linear isometries on the spaces (), the little Bloch space, and the group of surjective linear isometries on the big Bloch space are not supercyclic. Also, we observe that the groups of all surjective linear isometries on the Hardy space or the Bergman space (, ) are not supercyclic....
Let ℳ be a hyperfinite finite von Nemann algebra and be an increasing filtration of finite-dimensional von Neumann subalgebras of ℳ. We investigate abstract fractional integrals associated to the filtration . For a finite noncommutative martingale adapted to and 0 < α < 1, the fractional integral of x of order α is defined by setting for an appropriate sequence of scalars. For the case of a noncommutative dyadic martingale in L₁() where is the type II₁ hyperfinite factor equipped...