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On the spectral multiplicity of a direct sum of operators

M. T. Karaev (2006)

Colloquium Mathematicae

We calculate the spectral multiplicity of the direct sum T⊕ A of a weighted shift operator T on a Banach space Y which is continuously embedded in l p and a suitable bounded linear operator A on a Banach space X.

On the spectral properties of translation operators in one-dimensional tubes

Wojciech Hyb (1991)

Annales Polonici Mathematici

We study the spectral properties of some group of unitary operators in the Hilbert space of square Lebesgue integrable holomorphic functions on a one-dimensional tube (see formula (1)). Applying the Genchev transform ([2], [5]) we prove that this group has continuous simple spectrum (Theorem 4) and that the projection-valued measure for this group has a very explicit form (Theorem 5).

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