On operators with unitary ϱ-dilations
Annales Polonici Mathematici (1997)
- Volume: 66, Issue: 1, page 11-14
- ISSN: 0066-2216
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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
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- [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
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