Invertible weighted shift operators which are -isometries

Authors:
Muneo Chō, Schôichi Ôta and Kôtarô Tanahashi

Journal:
Proc. Amer. Math. Soc. **141** (2013), 4241-4247

MSC (2010):
Primary 47B37

DOI:
https://doi.org/10.1090/S0002-9939-2013-11701-6

Published electronically:
August 5, 2013

MathSciNet review:
3105867

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Abstract | References | Similar Articles | Additional Information

Abstract: For a bounded linear operator on a complex Hilbert space , let . is called an -isometry if . In this paper, for every even number , we give an example of invertible -isometry which is not an -isometry. Next we show that if is an -isometry, then the operator is not invertible.

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Additional Information

**Muneo Chō**

Affiliation:
Department of Mathematics, Kanagawa University, Yokohama 221-8686, Japan

Email:
chiyom01@kanagawa-u.ac.jp

**Schôichi Ôta**

Affiliation:
Department of Content and Creative Design, Kyushu University, Fukuoka 815-8540, Japan

Email:
ota@design.kyushu-u.ac.jp

**Kôtarô Tanahashi**

Affiliation:
Department of Mathematics, Tohoku Pharmaceutical University, Sendai 981-8558, Japan

Email:
tanahasi@tohoku-pharm.ac.jp

DOI:
https://doi.org/10.1090/S0002-9939-2013-11701-6

Keywords:
Hilbert space,
$m$-isometry,
bilateral weighted shift

Received by editor(s):
October 2, 2011

Received by editor(s) in revised form:
January 31, 2012

Published electronically:
August 5, 2013

Additional Notes:
The first author’s research was partially supported by Grant-in-Aid for Scientific Research, No. 20540192

The second author’s research was partially supported by Grant-in-Aid for Scientific Research, No. 20540178

The third author’s research was partially supported by Grant-in-Aid for Scientific Research, No. 20540184

Communicated by:
Richard Rochberg

Article copyright:
© Copyright 2013
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.