Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

DOI QR Code

QUASI-INNER FUNCTIONS OF A GENERALIZED BEURLING'S THEOREM

  • Kim, Yun-Su (Department of Mathematics The University of Toledo)
  • Published : 2009.11.30
Download PDF
⟨ Previous Next ⟩

Abstract

We introduce two kinds of quasi-inner functions. Since every rationally invariant subspace for a shift operator S$_K$ on a vector-valued Hardy space H$^2$(${\Omega}$, K) is generated by a quasi-inner function, we also provide relationships of quasi-inner functions by comparing rationally invariant subspaces generated by them. Furthermore, we discuss fundamental properties of quasi-inner functions and quasi-inner divisors.

Keywords

References

  1. H. Bercovici, Operator Theory and Arithmetic in $H^{\infty}$, Mathematical Surveys and Monographs, 26. American Mathematical Society, Providence, RI, 1988
  2. A. Beurling, On two problems concerning linear transformations in Hilbert space, Acta Math. 81 (1948), 17 pp https://doi.org/10.1007/BF02395019
  3. Paul R. Halmos, A Hilbert Space Problem Book, van Nostrand-Reinhold, Princeton, New Jersey, 1967
  4. Y. S. Kim, Linear algebraic properties for Jordan models of $C_o$-operators relative to multiply connected domains, J. Operator Theory 57 (2007), no. 2, 375-389
  5. W. Rudin, Analytic functions of class $H_p$, Trans. Amer. Math. Soc. 78 (1955), 46-66 https://doi.org/10.2307/1992948
  6. B. Sz.-Nagy and C. Foias, Harmonic Analysis of Operators on Hilbert Space, North- Holland, Amsterdam, 1970
  7. A. Zucchi, Operators of class $C_o$ with spectra in multiply connected regions, Mem. Amer. Math. Soc. 127 (1997), no. 607, viii+52 pp