Linear Modulus of a Linear Operator
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If φ is an analytic function mapping the unit disk D into itself, the composition operator Cφ is the operator on H 2 given by Cφf = f ◦φ. The structure of the composition operator Cφ is usually complex, even if the function φ is fairly simple. In this paper, we consider compositi
Abstract In this paper we have obtained the adjoint of an arbitrary operator (linear and nonlinear) in Hilbert space by introducing n-dimensional Riemannian manifold. This general formalism covers every linear operator (non – dif-ferential) in Hilbert space. In fact, our approach
This paper is a continuation of [5]. We apply the upper envelope representation method (or the quasilinearization method) in vector lattices developed in [4, 5] to the homogeneous functional calculus of linear and bilinear operators. Explicit formulae for computing φ̂(T1, . . . ,
We obtain a representation for the norm of the composition operator Cφ on the Hardy space H 2 whenever φ is a linear-fractional mapping of the form φ(z) = b/(cz + d). The representation shows that, for such mappings φ, the norm of Cφ always exceeds the essential norm of Cφ. Moreo