Operators on a Hilbert space similar to a part of the backward shift of multiplicity one

Yoichi Uetake

Operators on a Hilbert space similar to a part of the backward shift of multiplicity one

Yoichi Uetake

Studia Mathematica (2001)

Volume: 147, Issue: 1, page 27-35
ISSN: 0039-3223

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Abstract

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Let A: X → X be a bounded operator on a separable complex Hilbert space X with an inner product

⟨ \cdot, \cdot ⟩_{X}

. For b, c ∈ X, a weak resolvent of A is the complex function of the form

⟨ {(I - z A)}^{- 1} b, 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.

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Yoichi Uetake. "Operators on a Hilbert space similar to a part of the backward shift of multiplicity one." Studia Mathematica 147.1 (2001): 27-35. <http://eudml.org/doc/284978>.

@article{YoichiUetake2001,
abstract = {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 $⟨(I-zA)^\{-1\}b,c⟩_\{X\}$. 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.},
author = {Yoichi Uetake},
journal = {Studia Mathematica},
keywords = {inner product; similar; backward shift of multiplicity 1},
language = {eng},
number = {1},
pages = {27-35},
title = {Operators on a Hilbert space similar to a part of the backward shift of multiplicity one},
url = {http://eudml.org/doc/284978},
volume = {147},
year = {2001},
}

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
VL - 147
IS - 1
SP - 27
EP - 35
AB - 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 $⟨(I-zA)^{-1}b,c⟩_{X}$. 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.
LA - eng
KW - inner product; similar; backward shift of multiplicity 1
UR - http://eudml.org/doc/284978
ER -

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