### Subnormal operators of Hardy type

K. Rudol (1997)

Banach Center Publications

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K. Rudol (1997)

Banach Center Publications

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Dmitry V. Yakubovich (1998)

Revista Matemática Iberoamericana

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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...

Kitchen, J.W., Robbins, D.A. (1993)

International Journal of Mathematics and Mathematical Sciences

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K. Seddighi (1994)

Studia Mathematica

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Let ${M}_{z}$ be the operator of multiplication by z on a Banach space of functions analytic on a plane domain G. We say that ${M}_{z}$ is polynomially bounded if $\parallel {M}_{p}\parallel \le C\parallel p{\parallel}_{G}$ for every polynomial p. We give necessary and sufficient conditions for ${M}_{z}$ to be polynomially bounded. We also characterize the finite-codimensional invariant subspaces and derive some spectral properties of the multiplication operator in case the underlying space is Hilbert.

Peter Rosenthal (1982)

Banach Center Publications

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Peetre, Jaak

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Carl C. Cowen, Eva A. Gallardo-Gutiérrez (2016)

Concrete Operators

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The Invariant Subspace Problem for Hilbert spaces is a long-standing question and the use of universal operators in the sense of Rota has been an important tool for studying such important problem. In this survey, we focus on Rota’s universal operators, pointing out their main properties and exhibiting some old and recent examples.

David Stegenga (1975)

Annales de l'institut Fourier

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We show that a theorem of Rudin, concerning the sum of closed subspaces in a Banach space, has a converse. By means of an example we show that the result is in the nature of best possible.