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Composition-operator-preserving maps

Journal Name:

  • Mathematica Æterna

Publication Year:

  • 2011

Key Words:

Author NameFaculty of Author
Abstract (2. Language): 
For a given space X of holomorphic functions in the open unit disc, we determine which self-maps © of L(X) preserve the family FC(X) of composition operators leaving X invariant. We show that their surjective multiplicative restrictions to FC(X) are exactly of the form ©(T) = A¡1TA with A a bijective member of FC(X): We characterize the norm- preserving ones by the same form with A induced by a rotation. We generalize these results to the semi-multiplicative maps.
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  • 5
279-295
  • English

REFERENCES

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