Continuous and holomorphic functions with values in closed operators
Functional Analysis
2015-06-17 v3 Mathematical Physics
math.MP
Spectral Theory
Abstract
We systematically derive general properties of continuous and holomorphic functions with values in closed operators, allowing in particular for operators with empty resolvent set. We provide criteria for a given operator-valued function to be continuous or holomorphic. This includes sufficient conditions for the sum and product of operator-valued holomorphic functions to be holomorphic. Using graphs of operators, operator-valued functions are identified with functions with values in subspaces of a Banach space. A special role is thus played by projections onto closed subspaces of a Banach space, which depend holomorphically on a parameter.
Cite
@article{arxiv.1309.0164,
title = {Continuous and holomorphic functions with values in closed operators},
author = {Jan Dereziński and Michał Wrochna},
journal= {arXiv preprint arXiv:1309.0164},
year = {2015}
}
Comments
final version, introduction reworked, 25 p