%0 Journal Article
%T Continuous and holomorphic functions with values in closed operators
%A Jan Derezi¨½ski
%A Micha£¿ Wrochna
%J Mathematics
%D 2013
%I arXiv
%R 10.1063/1.4891759
%X 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.
%U http://arxiv.org/abs/1309.0164v3