Abstract
We study the adjointness problem for the closed extensions of a general b -elliptic operator A ∈ x -ν Diff m b ( M ; E ), ν > 0, initially defined as an unbounded operator A : C ∞ c ( M ; E ) ∈ x μ L 2 b ( M ; E ) → x μ L 2 b ( M ; E ), μ ∈ [inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="01i" /]. The case where A is a symmetric semibounded operator is of particular interest, and we give a complete description of the domain of the Friedrichs extension of such an operator.
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