Spectral properties of doubly commuting hyponormal operators
Spectral Theory and Sheaf Theory. II.
Spectrum of class operators.
Subnormal operators, cyclic vectors and reductivity
Two characterizations of the reductivity of a cyclic normal operator in Hilbert space are proved: the equality of the sets of cyclic and *-cyclic vectors, and the equality L²(μ) = P²(μ) for every measure μ equivalent to the scalar-valued spectral measure of the operator. A cyclic subnormal operator is reductive if and only if the first condition is satisfied. Several consequences are also presented.
Subnormal operators of finite type I. Xia's model and real algebraic curves in C2.
Xia proves in [9] that a pure subnormal operator S is completely determined by its self-commutator C = S*S - SS*, restricted to the closure M of its range and the operator Λ = (S*|M)*. In [9], [10], [11] he constructs a model for S that involves this two operators and the so-called mosaic, which is a projection-valued function, analytic outside the spectrum of the minimal normal extension of S. He finds all pure subnormals S with rank C = 2. We will give a complete description of pairs of matrices...
Subnormal operators of finite type II. Structure theorems.
This paper concerns pure subnormal operators with finite rank self-commutator, which we call subnormal operators of finite type. We analyze Xia's theory of these operators [21]-[23] and give its alternative exposition. Our exposition is based on the explicit use of a certain algebraic curve in C2, which we call the discriminant curve of a subnormal operator, and the approach of dual analytic similarity models of [26]. We give a complete structure result for subnormal operators of finite type, which...
Subnormal operators of Hardy type
Subnormal operators with compact selfcommutator.
Subnormality and cyclicity
For an unbounded operator S the question whether its subnormality can be built up from that of every , the restriction of S to a cyclic space generated by f in the domain of S, is analyzed. Though the question at large has been left open some partial results are presented and a possible way to prove it is suggested as well.
Subnormality from bounded vectors
Subnormality versus restrictions