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Geodesic neighborhoods in unitary orbits of self-adjoint operators of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.svg"><mml:mi mathvariant="script">K</mml:mi><mml:mo linebreak="goodbreak" linebreakstyle="after">+</mml:mo><mml:mi mathvariant="double-struck">C</mml:mi></mml:math>