MULTIPLICATION OPERATORS ON INVARIANT SUBSPACES OF FUNCTION SPACES

doi:10.1016/S0252-9602(13)60096-X

Abstract

Abstract:

Let M_φ 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 M_z, we derive some spectral properties of the multiplication operator M_φ : 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

B. YOUSEFI, Sh. KHOSHDEL, Y. JAHANSHAHI. MULTIPLICATION OPERATORS ON INVARIANT SUBSPACES OF FUNCTION SPACES[J].Acta mathematica scientia,Series B, 2013, 33(5): 1463-1470.

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