On operators with unitary ϱ-dilations

• Autorzy: T. Ando , K. Takahashi
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

polynomially bounded operators; operators of class $C_ϱ$; unitary ϱ-dilation

Kategorie tematyczne

• 47A20: Dilations, extensions, compressions

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 1997
• Tom: 66
• Numer: 1
• Strony: 11-14

Daty

wydano

1997

otrzymano

1995-02-15

Twórcy

autor

T. Ando

• Faculty of Economics, Hokusei Gakuen University, Atsubetsu-ku, Sapporo 004, Japan

autor

K. Takahashi

• Department of Mathematics, Hokkaido University, Sapporo 060, Japan

Bibliografia

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• [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.
• [6] H. Watanabe, Operators characterized by certain Cauchy-Schwarz type inequalities, Publ. Res. Inst. Math. Sci. 30 (1994), 249-259.