Operators on a Hilbert space similar to a part of the backward shift of multiplicity one
Yoichi Uetake
Studia Mathematica, Tome 147 (2001), p. 27-35 / Harvested from The Polish Digital Mathematics Library
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Let A: X → X be a bounded operator on a separable complex Hilbert space X with an inner product ⟨·,·⟩X. For b, c ∈ X, a weak resolvent of A is the complex function of the form ⟨(I-zA)-1b,c⟩X. We will discuss an equivalent condition, in terms of weak resolvents, for A to be similar to a restriction of the backward shift of multiplicity 1.

Publié le : 2001-01-01
EUDML-ID : urn:eudml:doc:284978 
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Yoichi Uetake. Operators on a Hilbert space similar to a part of the backward shift of multiplicity one. Studia Mathematica, Tome 147 (2001) pp. 27-35. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm147-1-3/