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Cyclic Vectors

  • Paul R. Halmos
Part of the Graduate Texts in Mathematics book series (GTM, volume 19)

Abstract

Consider first the simple unilateral shift U. Let 〈ξ0, ξ1, ξ2, ⋯〉 be a sequence of complex numbers such that
$$ \mathop {\lim }\limits_k \frac{1}{{{{\left| {{\xi _k}} \right|}^2}}}\sum\limits_{n = 1}^\infty {{{\left| {{\xi _{n + k}}} \right|}^2}} = 0. $$

Keywords

Position Operator Preceding Paragraph Linear Manifold Cyclic Vector Bounded Measurable Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag New York Inc. 1982

Authors and Affiliations

  • Paul R. Halmos

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