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Some properties of N-supercyclic operators

P. S. Bourdon, N. S. Feldman, J. H. Shapiro (2004)

Studia Mathematica

Let T be a continuous linear operator on a Hausdorff topological vector space 𝓧 over the field ℂ. We show that if T is N-supercyclic, i.e., if 𝓧 has an N-dimensional subspace whose orbit under T is dense in 𝓧, then T* has at most N eigenvalues (counting geometric multiplicity). We then show that N-supercyclicity cannot occur nontrivially in the finite-dimensional setting: the orbit of an N-dimensional subspace cannot be dense in an (N+1)-dimensional space. Finally, we show that a subnormal operator...

Sous-normalité jointe non bornée et applications

Olivier Demanze (2005)

Studia Mathematica

T. Trent gave a new characterization of subnormality for an operator on a Hilbert space. T. Bînzar and D. Păunescu generalized this condition to commuting triples of operators. Here, we give an n-variable unbounded version of the above results. Theorems of this kind have also been obtained by Z. J. Jabłoński and J. Stochel.

Spectra of subnormal Hardy type operators

K. Rudol (1997)

Annales Polonici Mathematici

The essential spectrum of bundle shifts over Parreau-Widom domains is studied. Such shifts are models for subnormal operators of special (Hardy) type considered earlier in [AD], [R1] and [R2]. By relating a subnormal operator to the fiber of the maximal ideal space, an application to cluster values of bounded analytic functions is obtained.

Subnormal operators, cyclic vectors and reductivity

Béla Nagy (2013)

Studia Mathematica

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.

Dmitry V. Yakubovich (1998)

Revista Matemática Iberoamericana

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.

Dmitry V. Yakubovich (1998)

Revista Matemática Iberoamericana

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...

Subnormality and cyclicity

Franciszek Hugon Szafraniec (2005)

Banach Center Publications

For an unbounded operator S the question whether its subnormality can be built up from that of every S f , 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.

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