Subnormal Operators

  • Paul R. Halmos
Part of the Graduate Texts in Mathematics book series (GTM, volume 19)


Every known proof of Fuglede’s theorem can be modified so as to yield this generalized conclusion. Alternatively, there is a neat derivation, via operator matrices, of the statement for two normal operators from the statement for one. Write
$$ \hat A = \left( {\begin{array}{*{20}{c}} {{A_1}}&0\\ 0&{{A_2}} \end{array}} \right)and\hat B = \left( {\begin{array}{*{20}{c}} 0&B\\ 0&0 \end{array}} \right). $$


Orthogonal Complement Operator Matrice Partial Isometry Weighted Shift Normal Extension 
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© Springer-Verlag New York Inc. 1982

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  • Paul R. Halmos

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