Displaying similar documents to “Subnormal operators of finite type I. Xia's model and real algebraic curves in C2.”

Subnormal operators of finite type II. Structure theorems.

Dmitry V. Yakubovich (1998)

Revista Matemática Iberoamericana

Similarity:

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 C, 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...

An operator-theoretic approach to truncated moment problems

Raúl Curto (1997)

Banach Center Publications

Similarity:

We survey recent developments in operator theory and moment problems, beginning with the study of quadratic hyponormality for unilateral weighted shifts, its connections with truncated Hamburger, Stieltjes, Hausdorff and Toeplitz moment problems, and the subsequent proof that polynomially hyponormal operators need not be subnormal. We present a general elementary approach to truncated moment problems in one or several real or complex variables, based on matrix positivity and extension....

Commutativity of compact selfadjoint operators

G. Greiner, W. Ricker (1995)

Studia Mathematica

Similarity:

The relationship between the joint spectrum γ(A) of an n-tuple A = ( A 1 , . . . , A n ) of selfadjoint operators and the support of the corresponding Weyl calculus T(A) : f ↦ f(A) is discussed. It is shown that one always has γ(A) ⊂ supp (T(A)). Moreover, when the operators are compact, equality occurs if and only if the operators A j mutually commute. In the non-commuting case the equality fails badly: While γ(A) is countable, supp(T(A)) has to be an uncountable set. An example is given showing that, for non-compact...