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arXiv · 1309.0164

Continuous and holomorphic functions with values in closed operators

Jan Dereziński·Michał Wrochna
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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.

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BibTeXRIS

Jan Dereziński, Michał Wrochna. 2014-07-14. Continuous and holomorphic functions with values in closed operators. https://doi.org/10.1063/1.4891759

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