On the local spectra of seminormal operators
On the local spectra of seminormal operators
Two theorems on the local spectra of seminormal operators are deduced. In the first theorem it is shown that when <italic>T</italic> is hyponormal any solution of the equation <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="left-parenthesis upper T minus lamda right-parenthesis x left-parenthesis lamda right-parenthesis equals x"> <mml:semantics> <mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mi>T</mml:mi> <mml:mo>−</mml:mo> …