The Selection Theory for Monotone Uniformly Equi-Bobtail Operators on Separable Hilbert Spaces

Abstract

We establish that a uniformly bounded infinite system \(\left\{A_{\alpha } \right\}\) of monotone, uniformly continuous, uniformly equi-bobtail operators \(A_{\alpha } \; :\; K\to H\) on the separable Hilbert space admits a convergent subsequence \(\left\{A_{n} \right\}\subset \left\{A_{\alpha } \right\}\) and show that limit of this subsequence is a monotone operator  \(A^{M} \; :\; K\to H \).