For block Toeplitz operators with symbols of the form QΦ* (Q a finite Blaschke-Potapov product), subnormality implies the operator is normal or analytic in several cases, plus a sufficient condition when Φ* is not bounded type.
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Subnormal block Toeplitz operators
For block Toeplitz operators with symbols of the form QΦ* (Q a finite Blaschke-Potapov product), subnormality implies the operator is normal or analytic in several cases, plus a sufficient condition when Φ* is not bounded type.