# On operators with unitary ϱ-dilations

Annales Polonici Mathematici (1997)

- Volume: 66, Issue: 1, page 11-14
- ISSN: 0066-2216

## Access Full Article

top## Abstract

top## How to cite

topT. Ando, and K. Takahashi. "On operators with unitary ϱ-dilations." Annales Polonici Mathematici 66.1 (1997): 11-14. <http://eudml.org/doc/270021>.

@article{T1997,

abstract = {We show a polynomially boundend operator T is similar to a unitary operator if there is a singular unitary operator W and an injection X such that XT = WX. If, in addition, T is of class $C_ϱ$, then T itself is unitary.},

author = {T. Ando, K. Takahashi},

journal = {Annales Polonici Mathematici},

keywords = {polynomially bounded operators; operators of class $C_ϱ$; unitary ϱ-dilation; polynomially bounded operator; similar to a unitary operator; singular unitary operator},

language = {eng},

number = {1},

pages = {11-14},

title = {On operators with unitary ϱ-dilations},

url = {http://eudml.org/doc/270021},

volume = {66},

year = {1997},

}

TY - JOUR

AU - T. Ando

AU - K. Takahashi

TI - On operators with unitary ϱ-dilations

JO - Annales Polonici Mathematici

PY - 1997

VL - 66

IS - 1

SP - 11

EP - 14

AB - We show a polynomially boundend operator T is similar to a unitary operator if there is a singular unitary operator W and an injection X such that XT = WX. If, in addition, T is of class $C_ϱ$, then T itself is unitary.

LA - eng

KW - polynomially bounded operators; operators of class $C_ϱ$; unitary ϱ-dilation; polynomially bounded operator; similar to a unitary operator; singular unitary operator

UR - http://eudml.org/doc/270021

ER -

## References

top- [1] K. Hoffman, Banach Spaces of Analytic Functions, Prentice-Hall, Englewood Cliffs, N.J., 1962. Zbl0117.34001
- [2] W. Mlak, Algebraic polynomially bounded operators, Ann. Polon. Math. 29 (1974), 103-109. Zbl0292.47014
- [3] W. Mlak, Operator valued representations of function algebras, in: Linear Operators and Approximation II, Proc. Conf. Oberwolfach Math. Res. Inst., Internat. Ser. Numer. Math. 25, Birkhäuser, Basel, 1974, 49-79.
- [4] B. Sz.-Nagy, On uniformly bounded linear transformations in Hilbert space, Acta Sci. Math. (Szeged) 11 (1947), 152-157.
- [5] B. Sz.-Nagy and C. Foiaş, Harmonic Analysis of Operators on Hilbert Space, North-Holland, Amsterdam, 1970. Zbl0201.45003
- [6] H. Watanabe, Operators characterized by certain Cauchy-Schwarz type inequalities, Publ. Res. Inst. Math. Sci. 30 (1994), 249-259. Zbl0815.47028

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.