Division subspaces and integrable kernels

Intracule functional models. II. Analytically integrable kernels.

We present, within the framework of intracule functional theory (IFT), a class of kernels whose correlation integrals can be found in closed form. This approach affords three major advantages over other kernels that we have considered previously; ease of implementation, computational efficiency, and numerical stability. We show that even the simplest member of the class yields reasonable estima...

The Feichtinger Conjecture for Reproducing Kernels in Model Subspaces

We obtain two results concerning the Feichtinger conjecture for systems of normalized reproducing kernels in the model subspace KΘ = H 2 ⊖ ΘH of the Hardy space H, where Θ is an inner function. First, we verify the Feichtinger conjecture for the kernels k̃λn = kλn/‖kλn‖ under the assumption that sup n |Θ(λn)| < 1. Secondly, we prove the Feichtinger conjecture in the case where Θ is a one-compone...

Hyperinvariant subspaces and quasinilpotent operators

For a bounded linear operator on Hilbert space we define a sequence of the so-called weakly extremal vectors‎. ‎We study the properties of weakly extremal vectors and show that the orthogonality equation is valid for weakly extremal vectors‎. ‎Also we show that any quasinilpotent operator $T$ has an hypernoncyclic vector‎, ‎and so $T$ has a nontrivial hyperinvariant subspace‎.

ε-weakly Chebyshev subspaces and quotient spaces

Projections of normed linear spaces with closed subspaces of finite codimension as kernels

It follows from [1] and [7] that any closed n-codimensional subspace (n ≥ 1 integer) of a real Banach space X is the kernel of a projection X → X, of norm less than f(n) + ε (ε > 0 arbitrary), where f(n) = 2 + (n − 1) √ n + 2 n + 1 . We have f(n) < √ n for n > 1, and f(n) = √ n − 1 √ n + O (