Some highlights in the development of algebraic analysis
We study the reproducing kernel Hilbert space with kernel kd , where d is a positive integer and k is the reproducing kernel of the analytic Dirichlet space.
In this paper we consider the problem of finding upper bounds of certain matrix operators such as Hausdorff, Nörlund matrix, weighted mean and summability on sequence spaces and Lorentz sequence spaces , which was recently considered in [9] and [10] and similarly to [14] by Josip Pecaric, Ivan Peric and Rajko Roki. Also, this study is an extension of some works by G. Bennett on spaces, see [1] and [2].
Some invariant subspaces for the operators A and T acting on a Hilbert space H and satisfying T*AT ≤ A and A ≥ 0, are presented. Especially, the largest invariant subspace for A and T on which the equality T* AT = A occurs, is studied in connections to others invariant or reducing subspaces for A, or T. Such subspaces are related to the asymptotic form of the subspace quoted above, this form being obtained using the operator limit of the sequence {T*nATn; n ≥ 1}. More complete results are given...
The notion of local mean ergodicity is introduced. Some general locally mean ergodic theorems for linear and affine operators are presented. Locally mean ergodic theorems for affine operators whose linear parts are compact or similar to subnormal operators on a Hilbert space are given.
In this note, we investigate non-locally-convex topological vector spaces for which the closed graph theorem holds. In doing so, we introduce new classes of topological vector spaces. Our study includes a direct extension of Pták duality to the non-locally-convex situation.