Operators on a Hilbert space similar to a part
of the backward shift of multiplicity one
Studia Mathematica, Tome 147 (2001) no. 1, pp. 27-35
Let $A :X \to X$ be a bounded operator on a separable complex Hilbert space $X$ with an inner product $\langle \cdot , \cdot \rangle _X$. For $b, c \in X$, a weak resolvent of $A$ is the complex function of the form $\langle (I-zA)^{-1}b, c \rangle _X$. 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 $1$.
Keywords:
bounded operator separable complex hilbert space inner product langle cdot cdot rangle weak resolvent complex function form langle i za rangle discuss equivalent condition terms weak resolvents similar restriction backward shift multiplicity
Affiliations des auteurs :
Yoichi Uetake 1
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author = {Yoichi Uetake},
title = {Operators on a {Hilbert} space similar to a part
of the backward shift of multiplicity one},
journal = {Studia Mathematica},
pages = {27--35},
year = {2001},
volume = {147},
number = {1},
doi = {10.4064/sm147-1-3},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/sm147-1-3/}
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TY - JOUR AU - Yoichi Uetake TI - Operators on a Hilbert space similar to a part of the backward shift of multiplicity one JO - Studia Mathematica PY - 2001 SP - 27 EP - 35 VL - 147 IS - 1 UR - http://geodesic.mathdoc.fr/articles/10.4064/sm147-1-3/ DO - 10.4064/sm147-1-3 LA - en ID - 10_4064_sm147_1_3 ER -
Yoichi Uetake. Operators on a Hilbert space similar to a part of the backward shift of multiplicity one. Studia Mathematica, Tome 147 (2001) no. 1, pp. 27-35. doi: 10.4064/sm147-1-3
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