Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
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SOME PROPERTIES OF INVARIANT SUBSPACES IN BANACH SPACES OF ANALYTIC FUNCTIONS

  • Hedayatian, K. (Department of Mathematics, College of Sciences, Shiraz University) ;
  • Robati, B. Khani (Department of Mathematics, College of Sciences, Shiraz University)
  • Received : 2007.06.29
  • Accepted : 2007.08.28
  • Published : 2007.12.25
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Abstract

Let $\cal{B}$ be a reflexive Banach space of functions analytic on the open unit disc and M be an invariant subspace of the multiplication operator by the independent variable, $M_z$. Suppose that $\varphi\;\in\;\cal{H}^{\infty}$ and $M_{\varphi}$ : M ${\rightarrow}$ M, defined by $M_{\varphi}f={\varphi}f$, is the operator of multiplication by ${\varphi}$. We would like to investigate the spectrum and the essential spectrum of $M_{\varphi}$ and we are looking for the necessary and sufficient conditions for $M_{\varphi}$ to be a Fredholm operator. Also we give a sufficient condition for a sequence $\{w_n\}$ to be an interpolating sequence for $\cal{B}$. At last the commutant of $M_{\varphi}$ under certain conditions on M and ${\varphi}$ is determined.

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References

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