Automatic Boundedness of Adjointable Operators on Barreled VH-Spaces
Functional Analysis
2021-08-02 v1
Abstract
We consider the space of adjointable operators on barreled VH (Vector Hilbert) spaces and show that such operators are automatically bounded.This generalizes the well known corresponding result for locally Hilbert -modules.We pick a consequence of this result in the dilation theory of VH-spaces and show that, when barreled VH-spaces are considered, a certain boundedness condition for the existence of VH-space linearisations, equivalently, of reproducing kernel VH-spaces, is automatically satisfied.
Cite
@article{arxiv.2107.14547,
title = {Automatic Boundedness of Adjointable Operators on Barreled VH-Spaces},
author = {Serdar Ay},
journal= {arXiv preprint arXiv:2107.14547},
year = {2021}
}
Comments
21 pages. arXiv admin note: text overlap with arXiv:1507.06840, arXiv:1701.04740