Lifting strong commutants of unbounded subnormal operators
نویسندگان
چکیده
Various theorems on lifting strong commutants of unbounded sub-normal (as well as formally subnormal) operators are proved. It is shown that the strong symmetric commutant of a closed symmetric operator S lifts to the strong commutant of some tight selfadjoint extension of S. Strong symmetric commutants of orthogonal sums of subnormal operators are investigated. Examples of (unbounded) irreducible subnormals, pure subnormals with rich strong symmetric commutants and cyclic subnormals with highly nontrivial strong commutants are discussed.
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