Acta mathematica scientia,Series B ›› 2013, Vol. 33 ›› Issue (5): 1463-1470.doi: 10.1016/S0252-9602(13)60096-X

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MULTIPLICATION OPERATORS ON INVARIANT SUBSPACES OF FUNCTION SPACES

B. YOUSEFI|Sh. KHOSHDEL|Y. JAHANSHAHI   

  1. Department of Mathematics, Payame Noor University P. O. Box, 19395-3697, Tehran, Iran
  • Received:2011-03-10 Revised:2012-11-12 Online:2013-09-20 Published:2013-09-20

Abstract:

Let Mφ be the operator of multiplication by φ on a Hilbert space of functions analytic on the open unit disk. For an invariant subspace F for the multiplication operator Mz, we derive some spectral properties of the multiplication operator Mφ : F →F. We characterize norm, spectrum, essential norm and essential spectrum of such operators when F has the codimension n property with n ∈ {1, 2, …, +1}.

Key words: invariant subspace, Hilbert space of analytic functions, essential spectrum, essential norm, Fredholm operator, multiplication operator

CLC Number: 

  • 47B38
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